{"id":4002,"date":"2016-05-06T11:49:00","date_gmt":"2016-05-06T11:49:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-2\/"},"modified":"2018-05-08T11:09:34","modified_gmt":"2018-05-08T05:39:34","slug":"ncert-solutions-class-12-maths-exercise-13-2","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-2\/","title":{"rendered":"NCERT Solutions Class 12 Maths Exercise 13.2"},"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-13-2\/#_NCERT_Solutions_class_12_Maths_Probability\" >\u00a0NCERT 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-13-2\/#2_Two_cards_are_drawn_at_random_and_without_replacement_from_a_pack_of_52_playing_cards_Find_the_probability_that_both_the_cards_are_black\" >2. Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.<\/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-13-2\/#3_A_box_of_oranges_is_inspected_by_examining_three_randomly_selected_oranges_drawn_without_replacement_If_all_the_three_oranges_are_good_the_box_is_approved_for_sale_otherwise_it_is_rejected_Find_the_probability_that_a_box_containing_15_oranges_out_of_which_12_are_good_and_3_are_bad_ones_will_be_approved_for_sale\" >3. A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale otherwise it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.<\/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-13-2\/#4_A_fair_coin_and_an_unbiased_die_are_tossed_Let_A_be_the_event_%E2%80%98head_appears_on_the_coin_and_B_be_the_event_%E2%80%983_on_the_die_Check_whether_A_and_B_are_independent_events_or_not\" >4. A fair coin and an unbiased die are tossed. Let A be the event \u2018head appears on the coin\u2019 and B be the event \u20183 on the die\u2019. Check whether A and B are independent events or not.<\/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-13-2\/#5_A_die_marked_1_2_3_in_red_and_4_5_6_in_green_is_tossed_Let_A_be_the_event_%E2%80%98number_is_even_and_B_be_the_event_%E2%80%98number_is_red_Are_A_and_B_independent\" >5. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event \u2018number is even\u2019 and B be the event \u2018number is red\u2019. Are A and B independent?<\/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-13-2\/#6_Let_E_and_F_be_events_with_P_E_P_F_and_P_EF_Are_E_and_F_independent\" >6. Let E and F be events with P (E) = \u00a0P (F) = \u00a0and P (EF) = \u00a0Are E and F independent?<\/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-13-2\/#7_Given_that_the_events_A_and_B_are_such_that_P_A_P_AB_and_P_B_Find_if_they_are_i_mutually_exclusive_ii_independent\" >7. Given that the events A and B are such that P (A) = \u00a0P (AB) = \u00a0and P (B) = \u00a0Find \u00a0if they are (i) mutually exclusive, (ii) independent.<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#8_Let_A_and_B_independent_events_P_A_03_and_P_B_04_Find\" >8. Let A and B independent events, P (A) = 0.3 and P (B) = 0.4. Find:<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-2\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#9_If_A_and_B_are_two_events_such_that_P_A_P_B_and_P_AB_find_P_not_A_and_not_B\" >9. If A and B are two events such that P (A) = \u00a0P (B) = \u00a0and P (AB) = \u00a0find P (not A and not B).<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-3\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#10_Events_A_and_B_are_such_that_P_A_P_B_and_P_not_A_or_not_B_State_whether_A_and_B_are_independent\" >10. Events A and B are such that P (A) = \u00a0P (B) = \u00a0and P (not A or not B) = \u00a0State whether A and B are independent.<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-4\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#11_Given_two_independent_events_A_and_B_such_that_P_A_03_P_B_06_Find\" >11. Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find:<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-5\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#12_A_die_is_tossed_thrice_Find_the_probability_of_getting_an_odd_number_at_least_once\" >12. A die is tossed thrice. Find the probability of getting an odd number at least once.<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-6\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#13_Two_balls_are_drawn_at_random_with_replacement_from_a_box_containing_10_black_and_8_red_balls_Find_the_probability_that\" >13. Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that:<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-7\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#14_Probability_of_solving_specific_problem_independently_by_A_and_B_are_and_respectively_If_both_try_to_solve_the_problem_independently_find_the_probability_that\" >14. Probability of solving specific problem independently by A and B are \u00a0and \u00a0respectively. If both try to solve the problem independently, find the probability that:<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-8\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#15_One_card_is_drawn_at_random_from_a_well_shuffled_deck_of_52_cards_In_which_of_the_following_cases_are_the_events_E_and_F_independent\" >15. One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-9\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/a><\/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-13-2\/#16_In_a_hostel_60_of_the_students_read_Hindi_newspaper_40_read_English_newspaper_and_20_read_both_Hindi_and_English_newspapers_A_student_is_selected_at_random\" >16. In a hostel 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random.<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-10\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#Choose_the_correct_answer_in_the_following\" >Choose the correct answer in the following:<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-11\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#18_Two_events_A_and_B_are_said_to_be_independent_if\" >18. Two events A and B are said to be independent, if:<\/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-13-2\/#NCERT_Solutions_Class_12_Maths_Exercise_132-12\" >NCERT Solutions Class 12 Maths Exercise 13.2<\/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-13-2\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions Class 12 Maths Exercise 13.2 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<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/12%20Maths%20Book%20Part-02%20.jpg\" alt=\"NCERT Solutions Class 12 Maths Exercise 13.2\" width=\"175\" height=\"224\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"_NCERT_Solutions_class_12_Maths_Probability\"><\/span><strong>\u00a0<\/strong>NCERT Solutions class 12 Maths Probability<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. If P (A) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image001.png\" \/><\/strong><strong>\u00a0and P (B) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image002.png\" \/><\/strong><strong>\u00a0find P (A<\/strong><strong><img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image003.png\" \/><\/strong><strong>B) if A and B are independent events.<\/strong><\/p>\n<p><strong>Ans. <\/strong>As A and B are independent events.<\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image004.png\" \/>\u00a0= P (A). P (B)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image005.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"2_Two_cards_are_drawn_at_random_and_without_replacement_from_a_pack_of_52_playing_cards_Find_the_probability_that_both_the_cards_are_black\"><\/span><strong>2. Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> S = 52 cards<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image007.png\" \/>\u00a0= 52<\/p>\n<p>Two cards are drawn without replacement.<\/p>\n<p>A = {26 black cards} <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image008.png\" \/>\u00a0= 26<\/p>\n<p>P (A) = <img decoding=\"async\" style=\"height: 41px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image009.png\" \/><\/p>\n<p>P (A and B) = P (A). P (B) = <img decoding=\"async\" style=\"height: 41px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image010.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"3_A_box_of_oranges_is_inspected_by_examining_three_randomly_selected_oranges_drawn_without_replacement_If_all_the_three_oranges_are_good_the_box_is_approved_for_sale_otherwise_it_is_rejected_Find_the_probability_that_a_box_containing_15_oranges_out_of_which_12_are_good_and_3_are_bad_ones_will_be_approved_for_sale\"><\/span><strong>3. A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale otherwise it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> S = {12 good oranges, 3 bad oranges}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image007.png\" \/>\u00a0= 15<\/p>\n<p>P (a box is approved) = <img decoding=\"async\" style=\"height: 49px; width: 179px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image011.png\" \/><\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"4_A_fair_coin_and_an_unbiased_die_are_tossed_Let_A_be_the_event_%E2%80%98head_appears_on_the_coin_and_B_be_the_event_%E2%80%983_on_the_die_Check_whether_A_and_B_are_independent_events_or_not\"><\/span><strong>4. A fair coin and an unbiased die are tossed. Let A be the event \u2018head appears on the coin\u2019 and B be the event \u20183 on the die\u2019. Check whether A and B are independent events or not.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> S = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image007.png\" \/>\u00a0= 12<\/p>\n<p>A = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)} <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image008.png\" \/>\u00a0= 6<\/p>\n<p>P (A) = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image012.png\" \/><\/p>\n<p>B = {(H, 3)}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image013.png\" \/>\u00a0= 1<\/p>\n<p>P (B) = <img decoding=\"async\" style=\"height: 49px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image014.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\/Ex13.2\/image003.png\" \/>\u00a0B) = {(H, 3)}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image015.png\" \/>\u00a0= 1<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 49px; width: 181px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image017.png\" \/><\/p>\n<p>Again P (A). P (B) = <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image018.png\" \/><\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 27px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image019.png\" \/>\u00a0P (A). P (B)<\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"5_A_die_marked_1_2_3_in_red_and_4_5_6_in_green_is_tossed_Let_A_be_the_event_%E2%80%98number_is_even_and_B_be_the_event_%E2%80%98number_is_red_Are_A_and_B_independent\"><\/span><strong>5. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event \u2018number is even\u2019 and B be the event \u2018number is red\u2019. Are A and B independent?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> S = <img decoding=\"async\" style=\"height: 48px; width: 100px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image020.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image007.png\" \/>\u00a0= 6<\/p>\n<p>A = {2, 4, 6} <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image008.png\" \/>\u00a0= 3<\/p>\n<p>P (A) = <img decoding=\"async\" style=\"height: 49px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image021.png\" \/><\/p>\n<p>B = <img decoding=\"async\" style=\"height: 45px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image022.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image013.png\" \/>\u00a0= 3<\/p>\n<p>P (B) = <img decoding=\"async\" style=\"height: 49px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image023.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\/Ex13.2\/image003.png\" \/>\u00a0B) = {2} <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image015.png\" \/>\u00a0= 1<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 49px; width: 175px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image024.png\" \/><\/p>\n<p>Now P (A). P (B) = <img decoding=\"async\" style=\"height: 41px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image025.png\" \/><\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 27px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image026.png\" \/>\u00a0P (A). P (B)<\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"6_Let_E_and_F_be_events_with_P_E_P_F_and_P_EF_Are_E_and_F_independent\"><\/span><strong>6. Let E and F be events with P (E) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image027.png\" \/><\/strong><strong>\u00a0P (F) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image028.png\" \/><\/strong><strong>\u00a0and P (E<\/strong><strong><img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image003.png\" \/><\/strong><strong>F) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image029.png\" \/><\/strong><strong>\u00a0Are E and F independent?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> P (E) = <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image027.png\" \/>\u00a0P (F) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image028.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 41px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image030.png\" \/><\/p>\n<p>Now P (E). P (F) = <img decoding=\"async\" style=\"height: 41px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image031.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image032.png\" \/>\u00a0P (E). P (F)<\/p>\n<p>Therefore, E and F are not independent events.<\/p>\n<hr \/>\n<h4><span class=\"ez-toc-section\" id=\"7_Given_that_the_events_A_and_B_are_such_that_P_A_P_AB_and_P_B_Find_if_they_are_i_mutually_exclusive_ii_independent\"><\/span><strong>7. Given that the events A and B are such that P (A) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image033.png\" \/><\/strong><strong>\u00a0P (A<\/strong><strong><img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image034.png\" \/><\/strong><strong>B) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image001.png\" \/><\/strong><strong>\u00a0and P (B) = <\/strong><strong><img decoding=\"async\" style=\"height: 17px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image035.png\" \/><\/strong><strong>\u00a0Find <\/strong><strong><img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image036.png\" \/><\/strong><strong>\u00a0if they are (i) mutually exclusive, (ii) independent.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\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\/Ex13.2\/image033.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image037.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image001.png\" \/>, P (B) = <img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image036.png\" \/><\/p>\n<p>(i) A and B are mutually exclusive events.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image037.png\" \/>\u00a0= P (A) + P (B)<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image038.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 145px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image039.png\" \/><\/p>\n<p>(ii) A and B are independent events.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image037.png\" \/>\u00a0= P (A) + P (B) \u2013 P (A). P (B)<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image040.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image041.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image042.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image043.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"8_Let_A_and_B_independent_events_P_A_03_and_P_B_04_Find\"><\/span><strong>8. Let A and B independent events, P (A) = 0.3 and P (B) = 0.4. Find:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(A) P (A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image003.png\" \/>B)<\/strong><\/p>\n<p><strong>(B) P (A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image034.png\" \/>B)<\/strong><\/p>\n<p><strong>(C) P <img decoding=\"async\" style=\"height: 29px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image044.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>(D) P <img decoding=\"async\" style=\"height: 29px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image045.png\" \/><\/strong><\/p>\n<p><strong>Ans. <\/strong>P (A) = 0.3, P (B) = 0.4<\/p>\n<p>A and B are independent events.<\/p>\n<p><strong>(i) <\/strong><img decoding=\"async\" style=\"height: 27px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image019.png\" \/>\u00a0P (A). P (B) = 0.3 x 0.4 = 0.12<\/p>\n<p><strong>(ii) <\/strong><img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image037.png\" \/>\u00a0= P (A) + P (B) \u2013 P (A). P (B) = 0.03 + 0.4 \u2013 0.3 x 0.4 = 0.7 \u2013 0.12 = 0.58<\/p>\n<p><strong>(iii)<\/strong> P<img decoding=\"async\" style=\"height: 29px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image044.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image046.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image047.png\" \/>\u00a0= P (A) = 0.3<\/p>\n<p>(iv) P<img decoding=\"async\" style=\"height: 29px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image045.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image048.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image049.png\" \/>\u00a0= P (B) = 0.4<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-2\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"9_If_A_and_B_are_two_events_such_that_P_A_P_B_and_P_AB_find_P_not_A_and_not_B\"><\/span><strong>9. If A and B are two events such that P (A) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image050.png\" \/><\/strong><strong>\u00a0P (B) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image051.png\" \/><\/strong><strong>\u00a0and P (A<\/strong><strong><img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image003.png\" \/><\/strong><strong>B) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image052.png\" \/><\/strong><strong>\u00a0find P (not A and not B).<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\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\/Ex13.2\/image050.png\" \/>\u00a0P (B) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image033.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 93px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image053.png\" \/><\/p>\n<p>P (not A) = 1 \u2013 P (A) = <img decoding=\"async\" style=\"height: 41px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image054.png\" \/><\/p>\n<p>P (not B) = 1 \u2013 P (B) = <img decoding=\"async\" style=\"height: 41px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image055.png\" \/><\/p>\n<p>Now P (A). P (B) = <img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/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\/Ex13.2\/image016.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image004.png\" \/>\u00a0= P (A). P (B)<\/p>\n<p>Thus, A and B are independent events.<\/p>\n<p>Therefore, \u2018not A\u2019 and \u2018not B\u2019 are independent events.<\/p>\n<p>Hence, P (not A and not B) = P (not A). P (not B)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image057.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-3\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"10_Events_A_and_B_are_such_that_P_A_P_B_and_P_not_A_or_not_B_State_whether_A_and_B_are_independent\"><\/span><strong>10. Events A and B are such that P (A) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image033.png\" \/><\/strong><strong>\u00a0P (B) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image058.png\" \/><\/strong><strong>\u00a0and P (not A or not B) = <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image059.png\" \/><\/strong><strong>\u00a0State whether A and B are independent.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> <img decoding=\"async\" style=\"height: 32px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image060.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 41px; width: 113px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image061.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 41px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image062.png\" \/><\/p>\n<p>P (A) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image051.png\" \/>\u00a0\u00a0and P (B) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image058.png\" \/><\/p>\n<p>P (A). P (B) = <img decoding=\"async\" style=\"height: 41px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image063.png\" \/><\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 27px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image026.png\" \/>\u00a0P (A). P (B)<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-4\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"11_Given_two_independent_events_A_and_B_such_that_P_A_03_P_B_06_Find\"><\/span><strong>11. Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(A) P (A and B) <\/strong><\/p>\n<p><strong>(B) P (A and not B)<\/strong><\/p>\n<p><strong>(C) P (A or B) <\/strong><\/p>\n<p><strong>(D) P (neither A nor B)<\/strong><\/p>\n<p><strong>Ans. <\/strong>P (A) = 0.3, P (B) = 0.6<\/p>\n<p>A and B are independent events.<\/p>\n<p><strong>(i)<\/strong> P (A and B) = P (A). P (B) = 0.3 x 0.6 = 0.18<\/p>\n<p><strong>(ii)<\/strong> P (A and not B) = <img decoding=\"async\" style=\"height: 32px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image064.png\" \/>\u00a0= P (A) \u2013 <img decoding=\"async\" style=\"height: 27px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image004.png\" \/>\u00a0= 0.3 \u2013 0.18 = 0.12<\/p>\n<p><strong>(iii)<\/strong> P (A or B) = P (A) + P (B) \u2013 P (A and B) = 0.3 + 0.6 \u2013 0.18 = 0.9 \u2013 0.18 = 0.72<\/p>\n<p><strong>(iv)<\/strong> P (neither A nor B) = P [not (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image034.png\" \/>\u00a0B)] = 1 \u2013 P (A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image034.png\" \/>\u00a0B) = 1 \u2013 0.72 = 0.28<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-5\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"12_A_die_is_tossed_thrice_Find_the_probability_of_getting_an_odd_number_at_least_once\"><\/span><strong>12. A die is tossed thrice. Find the probability of getting an odd number at least once.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> S = {1, 2, 3, 4, 5, 6}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image007.png\" \/>\u00a0= 6<\/p>\n<p>Let A represents an odd number.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0A = {1, 3, 5}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image008.png\" \/>\u00a0= 3<\/p>\n<p>P (A) = <img decoding=\"async\" style=\"height: 49px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image021.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 32px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image065.png\" \/>\u00a0= 1 \u2013 P (A) = <img decoding=\"async\" style=\"height: 41px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image055.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image066.png\" \/>\u00a0= 3<\/p>\n<p>Now P (at least one success) = 1 \u2013 P (X = 0)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 49px; width: 128px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image067.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-6\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"13_Two_balls_are_drawn_at_random_with_replacement_from_a_box_containing_10_black_and_8_red_balls_Find_the_probability_that\"><\/span><strong>13. Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(i) both balls are red.<\/strong><\/p>\n<p><strong>(ii) first ball is black and second is red.<\/strong><\/p>\n<p><strong>(iii) one of them is black and other is red.<\/strong><\/p>\n<p><strong>Ans. <\/strong>S = (10 black balls, 8 red balls)<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image007.png\" \/>\u00a0= = 18<\/p>\n<p>Let drawing of a red ball be a success.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0A = {8 red balls} <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image008.png\" \/>\u00a0= 8<\/p>\n<p>P (A) = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image068.png\" \/><\/p>\n<p>And <img decoding=\"async\" style=\"height: 32px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image065.png\" \/>\u00a0= 1 \u2013 P (A) = <img decoding=\"async\" style=\"height: 41px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image069.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image066.png\" \/>\u00a0= 2<\/p>\n<p><strong>(i)<\/strong> P (both are red ball) = P (A). P (B) = <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image070.png\" \/><\/p>\n<p><strong>(ii)<\/strong> P (first is black ball and second is red) = <img decoding=\"async\" style=\"height: 32px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image065.png\" \/>. P (A) = <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image071.png\" \/><\/p>\n<p><strong>(iii)<\/strong> P (one of them is black and other is red) = <img decoding=\"async\" style=\"height: 32px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image065.png\" \/>. P (A) + P (A). <img decoding=\"async\" style=\"height: 32px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image065.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 120px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image072.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-7\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"14_Probability_of_solving_specific_problem_independently_by_A_and_B_are_and_respectively_If_both_try_to_solve_the_problem_independently_find_the_probability_that\"><\/span><strong>14. Probability of solving specific problem independently by A and B are <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image051.png\" \/><\/strong><strong>\u00a0and <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image073.png\" \/><\/strong><strong>\u00a0respectively. If both try to solve the problem independently, find the probability that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(i) the problem is solved.<\/strong><\/p>\n<p><strong>(ii) exactly one of them solves the problem.<\/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\/Ex13.2\/image033.png\" \/>\u00a0P (B) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image073.png\" \/>, <img decoding=\"async\" style=\"height: 32px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image065.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image055.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image074.png\" \/><\/p>\n<p><strong>(i)<\/strong> P (the problem is solved) = 1 \u2013 P (the problem is not solved)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 32px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image075.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 32px; width: 97px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image076.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 156px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image077.png\" \/><\/p>\n<p><strong>(ii)<\/strong> P (exactly one of them solves the problem) = P (A). <img decoding=\"async\" style=\"height: 32px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image078.png\" \/>\u00a0+ <img decoding=\"async\" style=\"height: 32px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image065.png\" \/>\u00a0. P (B)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 188px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image079.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-8\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"15_One_card_is_drawn_at_random_from_a_well_shuffled_deck_of_52_cards_In_which_of_the_following_cases_are_the_events_E_and_F_independent\"><\/span><strong>15. One card is drawn at random from a well shuffled deck of 52 cards. In which of the following cases are the events E and F independent?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> S = {All the 52 cards}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image007.png\" \/>\u00a0= 52<\/p>\n<p><strong>(i)<\/strong> E = {13 spades}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image080.png\" \/>\u00a0= 13<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0P (E) = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image081.png\" \/><\/p>\n<p>F = {4 aces}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image082.png\" \/>\u00a0= 4<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0P (F) = <img decoding=\"async\" style=\"height: 49px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image083.png\" \/><\/p>\n<p>Now E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image003.png\" \/>\u00a0F = {An ace of spade}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image084.png\" \/>\u00a0= 1<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image085.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image086.png\" \/><\/p>\n<p>Also, P(E). P(F) = <img decoding=\"async\" style=\"height: 41px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image087.png\" \/><\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 27px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image088.png\" \/>\u00a0= P(E). P(F)<\/p>\n<p>Hence, E and F are independent events.<\/p>\n<p><strong>(ii)<\/strong> E = {26 black cards} <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image080.png\" \/>\u00a0= 26<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0P (E) = <img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image089.png\" \/><\/p>\n<p>F = {4 kings} <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image082.png\" \/>\u00a0= 4<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0P (F) = <img decoding=\"async\" style=\"height: 49px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image083.png\" \/><\/p>\n<p>Now E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image003.png\" \/>\u00a0F = {2 black kings}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image084.png\" \/>\u00a0= 2<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image085.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image090.png\" \/><\/p>\n<p>Also, P(E). P(F) = <img decoding=\"async\" style=\"height: 41px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image091.png\" \/><\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 27px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image088.png\" \/>\u00a0= P(E). P(F)<\/p>\n<p>Hence, E and F are independent events.<\/p>\n<p><strong>(iii)<\/strong> E = {4 kings, 4 queens}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image080.png\" \/>\u00a0= 8<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0P (E) = <img decoding=\"async\" style=\"height: 49px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image092.png\" \/><\/p>\n<p>F = {4 queens, 4 jacks}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image082.png\" \/>\u00a0= 8<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0P (F) = <img decoding=\"async\" style=\"height: 49px; width: 105px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image093.png\" \/><\/p>\n<p>Now E <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image003.png\" \/>\u00a0F = {4 queens }<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image084.png\" \/>\u00a0= 4<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 49px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image085.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image094.png\" \/><\/p>\n<p>Also, P(E). P(F) = <img decoding=\"async\" style=\"height: 41px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image095.png\" \/><\/p>\n<p>Therefore, <img decoding=\"async\" style=\"height: 27px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image088.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image096.png\" \/>\u00a0P(E). P(F)<\/p>\n<p>Hence, E and F are not independent events.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-9\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"16_In_a_hostel_60_of_the_students_read_Hindi_newspaper_40_read_English_newspaper_and_20_read_both_Hindi_and_English_newspapers_A_student_is_selected_at_random\"><\/span><strong>16. In a hostel 60% of the students read Hindi newspaper, 40% read English newspaper and 20% read both Hindi and English newspapers. A student is selected at random.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(a) Find the probability that she reads neither Hindi nor English newspapers.<\/strong><\/p>\n<p><strong>(b) If she reads Hindi newspaper, find the probability that she reads English newspaper.<\/strong><\/p>\n<p><strong>(c) If she reads English newspapers, find the probability she reads Hindi newspaper.<\/strong><\/p>\n<p><strong>Ans. <\/strong>Let A represents the student reading Hindi newspaper and B represents the students reading English newspaper.<\/p>\n<p>P (A) = <img decoding=\"async\" style=\"height: 41px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image097.png\" \/>\u00a0P (B) = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image098.png\" \/>\u00a0and P (A and B) = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image099.png\" \/><\/p>\n<p><strong>(a)<\/strong> P (neither Hindi nor English newspaper is read) = 1 \u2013 P (A or B)<\/p>\n<p>= 1 \u2013 [P (A) + P (B) \u2013 P (A and B)]\n<p>= <img decoding=\"async\" style=\"height: 45px; width: 141px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image100.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image101.png\" \/><\/p>\n<p><strong>(b) <\/strong><img decoding=\"async\" style=\"height: 41px; width: 109px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image102.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 61px; width: 244px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image103.png\" \/><\/p>\n<p><strong>(c)<\/strong> P<img decoding=\"async\" style=\"height: 61px; width: 245px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image104.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-10\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"Choose_the_correct_answer_in_the_following\"><\/span><strong>Choose the correct answer in the following:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>17. The probability of obtaining an even prime number on each die when a pair of dice is rolled is:<\/strong><\/p>\n<p><strong>(A) 0 (B) <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image073.png\" \/>\u00a0\u00a0(C) <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image105.png\" \/>\u00a0(D) <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image106.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong><img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image007.png\" \/>\u00a0= 36<\/p>\n<p>Let A represents an even prime number on each dice.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image016.png\" \/>\u00a0\u00a0A = {22}<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image006.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.2\/image008.png\" \/>\u00a0= 1<\/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\/Ex13.2\/image107.png\" \/><\/p>\n<p>Hence option (D) is correct.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-11\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"18_Two_events_A_and_B_are_said_to_be_independent_if\"><\/span><strong>18. Two events A and B are said to be independent, if:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(A) A and B are mutually exclusive.<\/strong><\/p>\n<p><strong>(B) P (A\u2019B\u2019) = [1 \u2013 P (A)] [1 \u2013 P (B)]<\/strong><\/p>\n<p><strong>(C) P (A) = P (B)<\/strong><\/p>\n<p><strong>(D) P (A) + P (B) = 1<\/strong><\/p>\n<p><strong>Ans. <\/strong>P (A\u2019 and B\u2019)<\/p>\n<p>= [1 \u2013 P (A)] . [1 \u2013 P (B)]\n<p>= P (A\u2019). P (B\u2019)<\/p>\n<p>Hence, option (B) is correct<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Exercise_132-12\"><\/span>NCERT Solutions Class 12 Maths Exercise 13.2<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 13.2 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 13.2\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-2\/\" aria-label=\"More on NCERT Solutions Class 12 Maths Exercise 13.2\">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-4002","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 13.2 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 12 Maths Exercise 13.2 in PDF format for free download. 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