{"id":4539,"date":"2016-05-16T11:49:00","date_gmt":"2016-05-16T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/"},"modified":"2018-05-08T10:35:28","modified_gmt":"2018-05-08T05:05:28","slug":"ncert-solutions-class-12-maths-exercise-13-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 13.1"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Probability\" >NCERT Solutions class 12 Maths Probability<\/a><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><ul class='ez-toc-list-level-4' ><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#2_Compute_P_if_P_B_05_and_P_AB_032\" >2. Compute P\u00a0if P (B) = 0.5 and P (AB) = 0.32<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#3_If_P_A_08_P_B_05_and_P_04_find\" >3. If P (A) = 0.8, P (B) = 0.5 and P\u00a0= 0.4, find:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#4_Evaluate_P_AB_if_2P_A_P_B_and_P\" >4. Evaluate P (AB) if 2P (A) = P (B) = \u00a0and P\u00a0= \u00a0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-2\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#5_If_P_A_P_B_and_P_AB\" >5. If P (A) = \u00a0P (B) = \u00a0and P (AB) =<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-3\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#6_Determine_P_A_coin_is_tossed_three_times\" >6. Determine P : A coin is tossed three times.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-4\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#7_Determine_P_Two_coins_are_tossed_once\" >7. Determine P : Two coins are tossed once.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-5\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#8_Determine_P_A_dice_is_thrown_three_times\" >8. Determine P : A dice is thrown three times.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-6\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#9_Determine_Mother_father_and_son_line_up_at_random_for_a_family_picture\" >9. Determine : Mother, father and son line up at random for a family picture.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-7\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#10_A_black_and_a_red_die_are_rolled\" >10. A black and a red die are rolled.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-8\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#11_A_fair_die_is_rolled_Consider_events_E_1_3_5_F_2_3_and_G_2_3_4_5_Find\" >11. A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}. Find:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#12_Assume_that_each_child_born_is_equally_likely_to_be_a_boy_or_a_girl_If_a_family_has_two_children_what_is_the_conditional_probability_that_both_are_girls_given_that_i_the_youngest_is_a_girl_ii_at_least_one_is_a_girl\" >12. Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl (ii) at least one is a girl?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#13_An_instructor_has_a_test_bank_consisting_of_300_easy_TrueFalse_questions_200_difficult_TrueFalse_questions_500_easy_multiple_choice_questions_and_400_difficult_multiple_choice_questions_If_a_question_is_selected_at_random_from_the_test_bank_what_is_the_probability_that_it_will_be_an_easy_question_given_that_it_is_a_multiple_choice_question\" >13. An instructor has a test bank consisting of 300 easy True\/False questions, 200 difficult True\/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the test bank, what is the probability that it will be an easy question given that it is a multiple choice question?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-9\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#14_Given_that_the_two_numbers_appearing_on_throwing_two_dice_are_different_Find_the_probability_of_the_event_%E2%80%98the_sum_of_numbers_on_the_dice_is_4\" >14. Given that the two numbers appearing on throwing two dice are different. Find the probability of the event \u2018the sum of numbers on the dice is 4\u2019.<\/a><ul class='ez-toc-list-level-5' ><li class='ez-toc-heading-level-5'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#Let_A_represents_the_event_%E2%80%9Cthe_sum_of_numbers_on_the_dice_is_4%E2%80%9D_and_B_represents_the_event_%E2%80%9Cthe_two_numbers_appearing_on_throwing_two_dice_are_different%E2%80%9D\" >Let A represents the event \u201cthe sum of numbers on the dice is 4\u201d and B represents the event \u201cthe two numbers appearing on throwing two dice are different\u201d.<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#15_Consider_the_experiment_of_throwing_a_die_if_a_multiple_of_3_comes_up_throw_the_die_again_and_if_any_other_number_comes_toss_a_coin_Find_the_conditional_probability_of_the_event_%E2%80%9Cthe_coin_shows_a_tail%E2%80%9D_given_that_%E2%80%9Cat_least_one_die_shows_a_3%E2%80%9D\" >15. Consider the experiment of throwing a die, if a multiple of 3 comes up throw the die again and if any other number comes toss a coin. Find the conditional probability of the event \u201cthe coin shows a tail\u201d, given that \u201cat least one die shows a 3\u201d.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-10\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#In_each_of_the_following_choose_the_correct_answer\" >In each of the following choose the correct answer:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-11\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#17_If_A_and_B_are_events_such_that_P_P_then\" >17. If A and B are events such that P\u00a0= P, then:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#NCERT_Solutions_class_12_Maths_Exercise_131-12\" >NCERT Solutions class 12 Maths Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 13.1 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p><strong>Download\u00a0<a href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-12-mathematics-matrices\/1287\/ncert-solutions\/5\/\">NCERT solutions for\u00a0Probability\u00a0<\/a>as PDF.<\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Probability\"><\/span>NCERT Solutions class 12 Maths Probability<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. Given that E and F are events such that P (E) = 0.6, P (F) = 0.3 and P (E<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>F) = 0.02, find P (E<img decoding=\"async\" style=\"height: 27px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image002.png\" \/>) and P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image003.png\" \/>.<\/strong><\/p>\n<p><strong>Ans. <\/strong>Given: \u00a0P (E) = 0.6, P (F) = 0.3 and P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = 0.2<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image006.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 54px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image007.png\" \/><\/p>\n<p>And P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image003.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image008.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 54px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image009.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"2_Compute_P_if_P_B_05_and_P_AB_032\"><\/span><strong>2. Compute P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0if P (B) = 0.5 and P (A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>B) = 0.32<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Given: P (B) = 0.5, P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = 0.32<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image011.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image012.png\" \/>\u00a0= 0.64<\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"3_If_P_A_08_P_B_05_and_P_04_find\"><\/span><strong>3. If P (A) = 0.8, P (B) = 0.5 and P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image013.png\" \/>\u00a0= 0.4, find:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(i) P (A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>B)\u00a0 <\/strong><\/p>\n<p><strong>(ii) P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0 <\/strong><\/p>\n<p><strong>(iii) P (A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image014.png\" \/>B)<\/strong><\/p>\n<p><strong>Ans. (i) <\/strong>P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image013.png\" \/>\u00a0. P (A) = 0.4 x 0.8 = 0.32<\/p>\n<p><strong>(ii) <\/strong>P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image011.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image012.png\" \/>\u00a0= 0.64<\/p>\n<p><strong>(iii)<\/strong> P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image014.png\" \/>\u00a0B) = P(A) + P (B) \u2013 P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = 0.8 + 0.5 \u2013 0.32 = 0.98<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"4_Evaluate_P_AB_if_2P_A_P_B_and_P\"><\/span><strong>4. Evaluate P (A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>B) if 2P (A) = P (B) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image015.png\" \/>\u00a0and P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image016.png\" \/>\u00a0<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>Given: 2 P (A) = P (B) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image015.png\" \/>, P <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image017.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P (A) = <img decoding=\"async\" style=\"height: 41px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image018.png\" \/><\/p>\n<p>Now P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image013.png\" \/>\u00a0. P (B) = <img decoding=\"async\" style=\"height: 41px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image019.png\" \/><\/p>\n<p>And P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image014.png\" \/>\u00a0B) = P(A) + P (B) \u2013 P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = <img decoding=\"async\" style=\"height: 41px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image021.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-2\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"5_If_P_A_P_B_and_P_AB\"><\/span><strong>5. If P (A) = <img decoding=\"async\" style=\"height: 41px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image022.png\" \/>\u00a0P (B) = <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image023.png\" \/>\u00a0and P (A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image014.png\" \/>B) = <img decoding=\"async\" style=\"height: 41px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image024.png\" \/><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. (i)<\/strong> P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image014.png\" \/>\u00a0B) = P(A) + P (B) \u2013 P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 41px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image026.png\" \/>\u00a0P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = <img decoding=\"async\" style=\"height: 41px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image027.png\" \/><\/p>\n<p><strong>(ii)<\/strong> P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image011.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 60px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image028.png\" \/><\/p>\n<p><strong>(iii) <\/strong>P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image013.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image029.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 60px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image030.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-3\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"6_Determine_P_A_coin_is_tossed_three_times\"><\/span><strong>6. Determine P <img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>: A coin is tossed three times.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(i) E : heads on third toss, F : heads on first two tosses.<\/strong><\/p>\n<p><strong>(ii) E : at least two heads, F : at most two heads.<\/strong><\/p>\n<p><strong>(iii) E : at most two tails, F : at least one tail.<\/strong><\/p>\n<p><strong>Ans.<\/strong> A coin tossed three times, i.e.,<\/p>\n<p>S = (TTT, HTT, THT, TTH, HHT, HTH, THH, HHH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image031.png\" \/>\u00a0= 8<\/p>\n<p><strong>(i)<\/strong> E : heads on third toss<\/p>\n<p>E = (TTH, HTH, THH, HHH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image032.png\" \/><\/p>\n<p>P (E) = <img decoding=\"async\" style=\"height: 49px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image033.png\" \/><\/p>\n<p>F : heads on first two tosses<\/p>\n<p>F = (HHT, HHH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image034.png\" \/>\u00a0=2<\/p>\n<p>P (F) = <img decoding=\"async\" style=\"height: 49px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image035.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F = (HHH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image036.png\" \/>\u00a0(E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = 1<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image037.png\" \/><\/p>\n<p>And P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image038.png\" \/><\/p>\n<p><strong>(ii)<\/strong> E : at least two heads<\/p>\n<p>E = (HHT, HTH, THH, HHH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image032.png\" \/><\/p>\n<p>P (E) = <img decoding=\"async\" style=\"height: 49px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image033.png\" \/><\/p>\n<p>F : at most two heads<\/p>\n<p>F = (TTT, HTT, THT, TTH, HHT, HTH, THH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image034.png\" \/>\u00a0= 7<\/p>\n<p>P (F) = <img decoding=\"async\" style=\"height: 49px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image039.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F = (HHT, HTH, THH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image036.png\" \/>\u00a0(E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = 3<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image040.png\" \/><\/p>\n<p>And P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image041.png\" \/><\/p>\n<p><strong>(iii)<\/strong> E : at most two tails<\/p>\n<p>E = (HTT, THT, TTH, HHT, HTH, THH, HHH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image042.png\" \/><\/p>\n<p>P (E) = <img decoding=\"async\" style=\"height: 49px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image043.png\" \/><\/p>\n<p>F : at least one tail<\/p>\n<p>F = (TTT, HTT, THT, TTH, HHT, HTH, THH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image034.png\" \/>\u00a0= 7<\/p>\n<p>P (F) = <img decoding=\"async\" style=\"height: 49px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image039.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F = (HTT, THT, TTH, HHT, HTH, THH)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image036.png\" \/>\u00a0(E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = 6<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image044.png\" \/><\/p>\n<p>And P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image045.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-4\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"7_Determine_P_Two_coins_are_tossed_once\"><\/span><strong>7.<\/strong> <strong>Determine P <img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>: Two coins are tossed once.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(i) E : tail appears on one coin, F : one coin shows head.<\/strong><\/p>\n<p><strong>(ii) E : no tail appears, F : no head appears.<\/strong><\/p>\n<p><strong>Ans. <\/strong>S = (HH, TH, HT, TT)\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image031.png\" \/>\u00a0= 4<\/p>\n<p><strong>(i)<\/strong> E : tail appears on one coin<\/p>\n<p>E = (TH, HT)\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image046.png\" \/><\/p>\n<p>P (E) = <img decoding=\"async\" style=\"height: 49px; width: 92px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image047.png\" \/><\/p>\n<p>F : one coin shows head<\/p>\n<p>F = (TH, HT)\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image034.png\" \/>\u00a0= 2<\/p>\n<p>P (F) = <img decoding=\"async\" style=\"height: 49px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image048.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F = (TH, HT) <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image036.png\" \/>\u00a0(E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = 2<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = <img decoding=\"async\" style=\"height: 49px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image049.png\" \/><\/p>\n<p>And P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 59px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image050.png\" \/><\/p>\n<p><strong>(ii)<\/strong> E : no tail appears<\/p>\n<p>E = (HH)\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image051.png\" \/><\/p>\n<p>P (E) = <img decoding=\"async\" style=\"height: 49px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image052.png\" \/><\/p>\n<p>F : no head appears<\/p>\n<p>F = (TT)\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image034.png\" \/>\u00a0= 1<\/p>\n<p>P (F) = <img decoding=\"async\" style=\"height: 49px; width: 66px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image053.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F = <img decoding=\"async\" style=\"height: 21px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image054.png\" \/>\u00a0\u00a0\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image036.png\" \/>\u00a0(E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = 0<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = <img decoding=\"async\" style=\"height: 49px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image055.png\" \/><\/p>\n<p>And P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 59px; width: 133px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image050.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-5\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"8_Determine_P_A_dice_is_thrown_three_times\"><\/span><strong>8. Determine P <img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>: A dice is thrown three times.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses.<\/strong><\/p>\n<p><strong>Ans. <\/strong>Since a dice has six faces. Therefore <img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image031.png\" \/>\u00a0= 6 x 6 x 6 = 216<\/p>\n<p>E = (1, 2, 3, 4, 5, 6) x (1, 2, 3, 4, 5, 6) x (4)<\/p>\n<p>F = (6) x (5) x (1, 2, 3, 4, 5, 6)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image034.png\" \/>\u00a0= 1 x 1 x 6 = 6<\/p>\n<p>P (F) = <img decoding=\"async\" style=\"height: 49px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image056.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F = (6, 5, 4)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image036.png\" \/>\u00a0(E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = 1<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = <img decoding=\"async\" style=\"height: 49px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image057.png\" \/><\/p>\n<p>And P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image058.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-6\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"9_Determine_Mother_father_and_son_line_up_at_random_for_a_family_picture\"><\/span><strong>9.<\/strong> <strong>Determine <img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>: Mother, father and son line up at random for a family picture.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>E : Son on one end, F : Father in middle.<\/strong><\/p>\n<p><strong>Ans. <\/strong>S = (MFS, MSF, SFM, SMF, FMS, FSM)\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image059.png\" \/><\/p>\n<p>E : Son on one end<\/p>\n<p>E = (MFS, SFM, SMF, FMS)\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image032.png\" \/><\/p>\n<p>F : Father in middle<\/p>\n<p>F = (MFS, SFM)\u00a0\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image034.png\" \/>\u00a0= 2<\/p>\n<p>P (F) = <img decoding=\"async\" style=\"height: 49px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image060.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F = (MFS, SFM)\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image036.png\" \/>\u00a0(E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = 2<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = <img decoding=\"async\" style=\"height: 49px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image061.png\" \/><\/p>\n<p>And P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 135px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image062.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-7\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"10_A_black_and_a_red_die_are_rolled\"><\/span><strong>10. A black and a red die are rolled.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(a) Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.<\/strong><\/p>\n<p><strong>(b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.<\/strong><\/p>\n<p><strong>Ans. (a)<\/strong> <img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image031.png\" \/>\u00a0= 6 x 6 = 36<\/p>\n<p>Let A represents obtaining a sum greater than 9 and B represents black die resulted in a 5.<\/p>\n<p>A = (46, 64, 55, 36, 63, 45, 54, 65, 56, 66) <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image063.png\" \/>\u00a0= 10<\/p>\n<p>P (A) = <img decoding=\"async\" style=\"height: 49px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image064.png\" \/><\/p>\n<p>B = (51, 52, 53, 54, 55, 56)\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image065.png\" \/>\u00a0= 6<\/p>\n<p>P (B) = <img decoding=\"async\" style=\"height: 49px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image066.png\" \/><\/p>\n<p>A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B = (55, 56)\u00a0\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image067.png\" \/>\u00a0= 2<\/p>\n<p>P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image068.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 175px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image069.png\" \/><\/p>\n<p><strong>(b)<\/strong> Let A denoted the sum is 8<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0A = {(2, 6). (3, 5), (4, 4), (5, 3), (6, 2)}<\/p>\n<p>B = Red die results in a number less than 4, either first or second die is red<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0B = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),<\/p>\n<p>(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)}<\/p>\n<p>P (B) = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image070.png\" \/><\/p>\n<p>A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B = {(2, 6), (3, 5)\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image067.png\" \/>\u00a0= 2<\/p>\n<p>P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image068.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image071.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 60px; width: 180px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image072.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-8\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"11_A_fair_die_is_rolled_Consider_events_E_1_3_5_F_2_3_and_G_2_3_4_5_Find\"><\/span><strong>11.<\/strong> <strong>A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5}. Find:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(i) P <img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0and P <img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image003.png\" \/><\/strong><\/p>\n<p><strong>(ii) P <img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image073.png\" \/>\u00a0and P <img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image074.png\" \/><\/strong><\/p>\n<p><strong>(iii) P <img decoding=\"async\" style=\"height: 30px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image075.png\" \/>\u00a0and P <img decoding=\"async\" style=\"height: 30px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image076.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong>S = (1, 2, 3, 4, 5, 6)\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image031.png\" \/>\u00a0= 6<\/p>\n<p>E = (1, 3, 5)\u00a0 F = (2, 3)\u00a0 G = (2, 3, 4, 5)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image077.png\" \/>\u00a0= 3\u00a0 <img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image034.png\" \/>\u00a0= 2\u00a0 <img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image078.png\" \/>\u00a0= 4<\/p>\n<p><strong>(i)<\/strong> P (E) = <img decoding=\"async\" style=\"height: 49px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image079.png\" \/>\u00a0\u00a0\u00a0\u00a0P (F) = <img decoding=\"async\" style=\"height: 49px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image080.png\" \/><\/p>\n<p>E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F = (3)\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image081.png\" \/>\u00a0= 1<\/p>\n<p>P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image082.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image083.png\" \/>\u00a0and P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image003.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image084.png\" \/><\/p>\n<p><strong>(ii)<\/strong> P (E) = <img decoding=\"async\" style=\"height: 49px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image079.png\" \/>\u00a0\u00a0\u00a0\u00a0P (G) = <img decoding=\"async\" style=\"height: 49px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image085.png\" \/><\/p>\n<p>E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0G = (3, 5)\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image086.png\" \/>\u00a0= 2<\/p>\n<p>P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0G) = <img decoding=\"async\" style=\"height: 49px; width: 104px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image087.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image073.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 169px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image088.png\" \/>\u00a0and P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image074.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image089.png\" \/><\/p>\n<p><strong>(iii)<\/strong> P (G) = <img decoding=\"async\" style=\"height: 49px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image085.png\" \/><\/p>\n<p>E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image014.png\" \/>\u00a0F = (1, 2, 3, 5) and G (2, 3, 4, 5)<\/p>\n<p>(E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image014.png\" \/>\u00a0F) <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0G = (2, 3, 5)\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 30px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image090.png\" \/>\u00a0= 3<\/p>\n<p><img decoding=\"async\" style=\"height: 41px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image091.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image092.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image093.png\" \/><\/p>\n<p>Again E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F = (3)<\/p>\n<p>(E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0G = (3)\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 30px; width: 126px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image094.png\" \/>\u00a0= 1<\/p>\n<p><img decoding=\"async\" style=\"height: 41px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image095.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 69px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image096.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 187px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image097.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"12_Assume_that_each_child_born_is_equally_likely_to_be_a_boy_or_a_girl_If_a_family_has_two_children_what_is_the_conditional_probability_that_both_are_girls_given_that_i_the_youngest_is_a_girl_ii_at_least_one_is_a_girl\"><\/span><strong>12.<\/strong> <strong>Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that (i) the youngest is a girl (ii) at least one is a girl?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> Let first and second girl are denoted by G<sub>1<\/sub> and G<sub>2<\/sub> and boys B<sub>1<\/sub> and B<sub>2<\/sub>.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0S = {(G<sub>1<\/sub>G<sub>2<\/sub>), (G<sub>1<\/sub>B<sub>2<\/sub>), (G<sub>2<\/sub>B<sub>1<\/sub>), (B<sub>1<\/sub>B<sub>2<\/sub>)}<\/p>\n<p>Let A = Both the children are girls = (G<sub>1<\/sub>G<sub>2<\/sub>)<\/p>\n<p>B = Youngest child is girl = {(G<sub>1<\/sub>G<sub>2<\/sub>), (B<sub>1<\/sub>G<sub>2<\/sub>)}<\/p>\n<p>C = at least one is a girl = {(G<sub>1<\/sub>B<sub>2<\/sub>), (G<sub>1<\/sub>G<sub>2<\/sub>), (B<sub>1<\/sub>G<sub>2<\/sub>)}<\/p>\n<p>A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B = (G<sub>1<\/sub>G<sub>2<\/sub>)\u00a0\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0\u00a0P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image098.png\" \/><\/p>\n<p>A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0C = (G<sub>1<\/sub>G<sub>2<\/sub>)\u00a0\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0\u00a0P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0C) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image098.png\" \/><\/p>\n<p>P (B) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image099.png\" \/>\u00a0and P (C) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image100.png\" \/><\/p>\n<p><strong>(i)<\/strong> P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/> = <img decoding=\"async\" style=\"height: 59px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image101.png\" \/><\/p>\n<p><strong>(ii)<\/strong> P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image102.png\" \/> = <img decoding=\"async\" style=\"height: 60px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image103.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"13_An_instructor_has_a_test_bank_consisting_of_300_easy_TrueFalse_questions_200_difficult_TrueFalse_questions_500_easy_multiple_choice_questions_and_400_difficult_multiple_choice_questions_If_a_question_is_selected_at_random_from_the_test_bank_what_is_the_probability_that_it_will_be_an_easy_question_given_that_it_is_a_multiple_choice_question\"><\/span><strong>13. An instructor has a test bank consisting of 300 easy True\/False questions, 200 difficult True\/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the test bank, what is the probability that it will be an easy question given that it is a multiple choice question?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> Number of easy True\/False questions = 300<\/p>\n<p>Number of difficult True\/False questions = 200<\/p>\n<p>Number of easy multiple choice questions = 500<\/p>\n<p>Number of difficult multiple choice questions = 400<\/p>\n<p>Total number of all such questions = <img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image031.png\" \/>\u00a0= 1400<\/p>\n<p>Let E represents an easy question and F represents a multiple choice question.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image077.png\" \/>\u00a0= 300 + 500 = 800 and <img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image034.png\" \/>\u00a0= 500 + 400 = 900<\/p>\n<p>P (F) = <img decoding=\"async\" style=\"height: 49px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image104.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image081.png\" \/>\u00a0= 500\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0P (E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0F) = <img decoding=\"async\" style=\"height: 49px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image105.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image005.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 61px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image106.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-9\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"14_Given_that_the_two_numbers_appearing_on_throwing_two_dice_are_different_Find_the_probability_of_the_event_%E2%80%98the_sum_of_numbers_on_the_dice_is_4\"><\/span><strong>14. Given that the two numbers appearing on throwing two dice are different. Find the probability of the event \u2018the sum of numbers on the dice is 4\u2019.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> S = \u00a0(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1)<\/p>\n<p>(1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (6, 2)<\/p>\n<p>(1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (6, 3)<\/p>\n<p>(1, 4), (2, 4), (3, 4), (4, 4), (5, 4), (6, 4)<\/p>\n<p>(1, 5), (2, 5), (3, 5), (4, 5), (5, 5), (6, 5)<\/p>\n<p>(1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (6, 6)<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image031.png\" \/>\u00a0= 36<\/p>\n<h5><span class=\"ez-toc-section\" id=\"Let_A_represents_the_event_%E2%80%9Cthe_sum_of_numbers_on_the_dice_is_4%E2%80%9D_and_B_represents_the_event_%E2%80%9Cthe_two_numbers_appearing_on_throwing_two_dice_are_different%E2%80%9D\"><\/span>Let A represents the event \u201cthe sum of numbers on the dice is 4\u201d and B represents the event \u201cthe two numbers appearing on throwing two dice are different\u201d.<span class=\"ez-toc-section-end\"><\/span><\/h5>\n<p>Therefore, A = {(1, 3), (2, 2), (3, 1)} <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image063.png\" \/>\u00a0= 3<\/p>\n<p>P (A) = <img decoding=\"async\" style=\"height: 49px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image107.png\" \/><\/p>\n<p>Also B = {(2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (1, 2), (3, 2), (4, 2), (5, 2), (6, 2),(1, 3), (2, 3), (4, 3), (5, 3), (6, 3), (1, 4), (2, 4), (3, 4), (5, 4), (6, 4),(1, 5), (2, 5), (3, 5), (4, 5), (6, 5), (1, 6), (2, 6), (3, 6), (4, 6), (5, 6)}<\/p>\n<p><img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image065.png\" \/>\u00a0= 30<\/p>\n<p>P (B) = <img decoding=\"async\" style=\"height: 49px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image108.png\" \/><\/p>\n<p>Now A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B = {(1, 3), (3, 1)}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image067.png\" \/>\u00a0= 2<\/p>\n<p>P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = <img decoding=\"async\" style=\"height: 49px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image109.png\" \/><\/p>\n<p>Hence, P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image011.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 61px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image110.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"15_Consider_the_experiment_of_throwing_a_die_if_a_multiple_of_3_comes_up_throw_the_die_again_and_if_any_other_number_comes_toss_a_coin_Find_the_conditional_probability_of_the_event_%E2%80%9Cthe_coin_shows_a_tail%E2%80%9D_given_that_%E2%80%9Cat_least_one_die_shows_a_3%E2%80%9D\"><\/span><strong>15.<\/strong> <strong>Consider the experiment of throwing a die, if a multiple of 3 comes up throw the die again and if any other number comes toss a coin. Find the conditional probability of the event \u201cthe coin shows a tail\u201d, given that \u201cat least one die shows a 3\u201d.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans. <\/strong>S = {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)<\/p>\n<p>(1, H), (2, H), (3, H), (4, H), (5, H), (1, T), (2, T), (3, T), (4, T), (5, T)}<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image031.png\" \/>\u00a0= 20<\/p>\n<p>P (first die shows a multiple of 3) = <img decoding=\"async\" style=\"height: 41px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image111.png\" \/><\/p>\n<p>P (first die shows a number which is not a multiple of 3) = <img decoding=\"async\" style=\"height: 41px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image112.png\" \/><\/p>\n<p>Let A = the coin shows a tail = {(1, T), (2, T), (4, T), (5, T)}<\/p>\n<p>B = at least one die shows a 3 = {(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)}<\/p>\n<p>A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B = <img decoding=\"async\" style=\"height: 21px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image054.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image063.png\" \/>\u00a0= 4, <img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image065.png\" \/>\u00a0= 6, <img decoding=\"async\" style=\"height: 27px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image067.png\" \/>\u00a0= 0<\/p>\n<p>P (B) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image113.png\" \/>\u00a0\u00a0and P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>\u00a0B) = 0<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image114.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 52px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image115.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-10\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"In_each_of_the_following_choose_the_correct_answer\"><\/span><strong>In each of the following choose the correct answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>16.<\/strong> <strong>If P (A) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image116.png\" \/>\u00a0P (B) = 0, then P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0is:<\/strong><\/p>\n<p><strong>(A) 0\u00a0\u00a0 <\/strong><\/p>\n<p><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image117.png\" \/>\u00a0\u00a0\u00a0\u00a0<\/strong><\/p>\n<p><strong>(C) not defined <\/strong><\/p>\n<p><strong>(D) 1<\/strong><\/p>\n<p><strong>Ans.<\/strong> P (A) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image116.png\" \/>\u00a0P(B) = 0<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image118.png\" \/>\u00a0= 0<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image004.png\" \/>\u00a0P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image114.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image119.png\" \/>\u00a0= not defined<\/p>\n<p>Therefore, option (C) is correct.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-11\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"17_If_A_and_B_are_events_such_that_P_P_then\"><\/span><strong>17.<\/strong> <strong>If A and B are events such that P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/>\u00a0= P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image013.png\" \/>, then:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(A) A<img decoding=\"async\" style=\"height: 13px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image120.png\" \/>B\u00a0 <\/strong><\/p>\n<p><strong>(B) A = B\u00a0 <\/strong><\/p>\n<p><strong>(C) A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image001.png\" \/>B = <img decoding=\"async\" style=\"height: 21px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image054.png\" \/>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p><strong>(D) P (A) = P (B)<\/strong><\/p>\n<p><strong>Ans.<\/strong> P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image010.png\" \/> = P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image013.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 49px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image121.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.1\/image025.png\" \/>\u00a0P (A) = P (B)<\/p>\n<p>Therefore, option (D) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_131-12\"><\/span>NCERT Solutions class 12 Maths Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 13 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_App_for_Students\"><\/span>CBSE App for Students<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download\u00a0NCERT Solutions for class 12 Physics, Chemistry, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions class 12 Maths Exercise 13.1 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 &#8230; <a title=\"NCERT Solutions class 12 Maths Exercise 13.1\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-1\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 13.1\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1432,281],"tags":[283,1342,321,216],"class_list":["post-4539","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-12","category-ncert-solutions","tag-cbse-study-material","tag-class-12","tag-mathematics","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class 12 Maths Exercise 13.1 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 13.1 in PDF format for free download. 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