{"id":4542,"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-13-5\/"},"modified":"2018-05-08T11:43:50","modified_gmt":"2018-05-08T06:13:50","slug":"ncert-solutions-class-12-maths-exercise-13-5","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-5\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 13.5"},"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-13-5\/#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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#4_Five_cards_are_drawn_successively_with_replacement_from_a_well-shuffled_deck_of_52_cards_What_is_the_probability_that\" >4.\u00a0 Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that:<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-2\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#5_The_probability_that_a_bulb_produced_by_a_factory_will_fuse_after_150_days_of_use_is_005_Find_the_probability_that_out_of_5_such_bulbs\" >5.\u00a0 The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-3\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#6_A_bag_consists_of_10_balls_each_marked_with_one_of_the_digits_0_to_9_If_four_balls_are_drawn_successively_with_replacement_from_the_bag_what_is_the_probability_that_none_is_marked_with_the_digit_0\" >6.\u00a0 A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-4\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#7_In_an_examination_20_questions_of_true-false_are_asked_Suppose_a_student_tosses_a_fair_coin_to_determine_his_answer_to_each_question_If_the_coin_falls_heads_he_answers_%E2%80%98true_if_it_falls_tails_he_answers_%E2%80%98false_Find_the_probability_that_he_answers_at_least_12_questions_correctly\" >7.\u00a0 In an examination, 20 questions of true-false are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers \u2018true\u2019, if it falls tails, he answers \u2018false\u2019. Find the probability that he answers at least 12 questions correctly.<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-5\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#8_Suppose_X_has_a_binomial_distribution_B_Show_that_X_3_is_the_most_likely_outcome\" >8.\u00a0 Suppose X has a binomial distribution B. Show that X = 3 is the most likely outcome.<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-6\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#9_On_a_multiple_choice_examination_with_three_possible_answers_for_each_of_the_five_questions_what_is_the_probability_that_a_candidate_would_get_four_or_more_correct_answers_just_by_guessing\" >9.\u00a0 On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-7\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#10_A_person_buys_a_lottery_ticket_in_50_lotteries_in_each_of_which_his_chance_of_winning_a_prize_is_What_is_the_probability_that_he_will_win_a_prize\" >10.\u00a0 A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is \u00a0\u00a0What is the probability that he will win a prize:<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-8\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#11_Find_the_probability_of_getting_5_exactly_twice_in_7_throws_of_a_die\" >11.\u00a0 Find the probability of getting 5 exactly twice in 7 throws of a die.<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-9\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#12_Find_the_probability_of_throwing_at_most_2_sixes_in_6_throws_of_a_single_die\" >12.\u00a0 Find the probability of throwing at most 2 sixes in 6 throws of a single die.<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-10\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#13_It_is_known_that_10_of_certain_articles_manufactured_are_defective_What_is_the_probability_that_in_a_random_sample_of_12_such_articles_9_are_defective\" >13.\u00a0 It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?<\/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-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-11\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#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-24\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-12\" >NCERT Solutions class 12 Maths Exercise 13.5<\/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-13-5\/#15_In_a_box_containing_100_bulbs_10_are_defective_The_probability_that_out_of_a_sample_of_5_bulbs_none_is_defective_is\" >15.\u00a0 In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is:<\/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-26\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-5\/#NCERT_Solutions_class_12_Maths_Exercise_135-13\" >NCERT Solutions class 12 Maths Exercise 13.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-5\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 13.5 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 13.5\" width=\"187\" height=\"240\" \/><\/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 style=\"text-align: justify;\"><strong>1.\u00a0 A die is thrown 6 times. If \u2018getting an odd number\u2019 is a success, what is the probability of:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i)\u00a0 5 successes?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)\u00a0 at least 5 successes?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)\u00a0 at most 5 successes?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong>S = {1, 2, 3, 4, 5, 6}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image002.png\" \/>\u00a0= 6<\/p>\n<p style=\"text-align: justify;\">A = {1, 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\/Ex13.5\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image003.png\" \/>\u00a0= 3<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image004.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image005.png\" \/>\u00a0and\u00a0 <img decoding=\"async\" style=\"height: 41px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image007.png\" \/>\u00a0= 6 and P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = C<img decoding=\"async\" style=\"height: 27px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong>\u00a0 <img decoding=\"async\" style=\"height: 19px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image010.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 5) = C (6, 5) <img decoding=\"async\" style=\"height: 49px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image011.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image012.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong>\u00a0 <img decoding=\"async\" style=\"height: 21px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (at least 5 success) = P (X = 5) + P (X = 6) = <img decoding=\"async\" style=\"height: 49px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image014.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong>\u00a0 P (at most 5 success) = 1 \u2013 P (X = 6) = <img decoding=\"async\" style=\"height: 41px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image015.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>2.\u00a0 A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong><img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image002.png\" \/>\u00a0= 36, A = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image003.png\" \/>\u00a0= 6<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image004.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 103px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image016.png\" \/>\u00a0and\u00a0 <img decoding=\"async\" style=\"height: 41px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image007.png\" \/>\u00a0= 4 and <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>\u00a0= 2<\/p>\n<p style=\"text-align: justify;\">P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = C<img decoding=\"async\" style=\"height: 27px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 2) = C (4, 2) <img decoding=\"async\" style=\"height: 49px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image018.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image019.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>3.\u00a0 There are 5% defective items in a large bulk of items. What is the probability that a sample of 10 items will include not more than one defective item?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong><img decoding=\"async\" style=\"height: 41px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image020.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 147px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image021.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image007.png\" \/>\u00a0= 10, <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>\u00a0= 0, 1<\/p>\n<p style=\"text-align: justify;\">P (not more than one defective items) = P (X = 0) + P (X = 1)<\/p>\n<p style=\"text-align: justify;\">\u00a0 = C (10, 0) <img decoding=\"async\" style=\"height: 49px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image022.png\" \/>\u00a0+ C (10, 1) <img decoding=\"async\" style=\"height: 49px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image023.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0 = <img decoding=\"async\" style=\"height: 49px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image024.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Five_cards_are_drawn_successively_with_replacement_from_a_well-shuffled_deck_of_52_cards_What_is_the_probability_that\"><\/span><strong>4.\u00a0 Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>(i)\u00a0 all the five cards are spade?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)\u00a0 only 3 cards are spades?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)\u00a0 none is spade?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.<\/strong>\u00a0 S = 52 cards\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image002.png\" \/>\u00a0= 52 and A = {13 spades}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image003.png\" \/>\u00a013<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image025.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image007.png\" \/>\u00a0= 5, <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>\u00a0= 5<\/p>\n<p style=\"text-align: justify;\">P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = <img decoding=\"async\" style=\"height: 25px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 5) = <img decoding=\"async\" style=\"height: 49px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image007.png\" \/>\u00a0= 5, <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>\u00a0= 0<\/p>\n<p style=\"text-align: justify;\">P (X = 3) = <img decoding=\"async\" style=\"height: 49px; width: 308px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong>\u00a0 <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image007.png\" \/>\u00a0= 5, <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>\u00a0= 0<\/p>\n<p style=\"text-align: justify;\">P (X = 0) = <img decoding=\"async\" style=\"height: 49px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image030.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-2\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_The_probability_that_a_bulb_produced_by_a_factory_will_fuse_after_150_days_of_use_is_005_Find_the_probability_that_out_of_5_such_bulbs\"><\/span><strong>5.\u00a0 The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong><img decoding=\"async\" style=\"height: 17px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image004.png\" \/>\u00a0= 0.05 and <img decoding=\"async\" style=\"height: 17px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image031.png\" \/>\u00a0= 1 \u2013 0.05 = 0.96<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image007.png\" \/>\u00a0= 5 and P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = C<img decoding=\"async\" style=\"height: 27px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong>\u00a0 <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>\u00a0= 0<\/p>\n<p style=\"text-align: justify;\">P (X = 0) = C (5, 0), <img decoding=\"async\" style=\"height: 49px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image032.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong>\u00a0 Not more than one success<\/p>\n<p style=\"text-align: justify;\">P (not more than one success) = P (X = 0) + P (X = 1)<\/p>\n<p style=\"text-align: justify;\">\u00a0 = <img decoding=\"async\" style=\"height: 49px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image033.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0 = <img decoding=\"async\" style=\"height: 49px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0 = <img decoding=\"async\" style=\"height: 49px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image035.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0 = <img decoding=\"async\" style=\"height: 49px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image036.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong>\u00a0 P (more than one success) = 1 \u2013 [P (X = 0) + P (X = 1)]\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 29px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong>\u00a0 P (at least one success) = 1 \u2013 P (X = 0)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image038.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-3\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_A_bag_consists_of_10_balls_each_marked_with_one_of_the_digits_0_to_9_If_four_balls_are_drawn_successively_with_replacement_from_the_bag_what_is_the_probability_that_none_is_marked_with_the_digit_0\"><\/span><strong>6.\u00a0 A bag consists of 10 balls each marked with one of the digits 0 to 9. If four balls are drawn successively with replacement from the bag, what is the probability that none is marked with the digit 0?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong>S = {0, 1, 2 3, 4, 5, 6, 7, 8, 9}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image002.png\" \/>\u00a0= 10<\/p>\n<p style=\"text-align: justify;\">Let A represents that the ball is marked with the digit 0.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image039.png\" \/>\u00a0A = {0}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image003.png\" \/>\u00a0= 1<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image040.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image041.png\" \/><\/p>\n<p style=\"text-align: justify;\">\u00a0 <img decoding=\"async\" style=\"height: 21px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image042.png\" \/>\u00a0and P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = <img decoding=\"async\" style=\"height: 25px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now P (one is marked with its digit 0) = <img decoding=\"async\" style=\"height: 49px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image043.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-4\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_In_an_examination_20_questions_of_true-false_are_asked_Suppose_a_student_tosses_a_fair_coin_to_determine_his_answer_to_each_question_If_the_coin_falls_heads_he_answers_%E2%80%98true_if_it_falls_tails_he_answers_%E2%80%98false_Find_the_probability_that_he_answers_at_least_12_questions_correctly\"><\/span><strong>7.\u00a0 In an examination, 20 questions of true-false are asked. Suppose a student tosses a fair coin to determine his answer to each question. If the coin falls heads, he answers \u2018true\u2019, if it falls tails, he answers \u2018false\u2019. Find the probability that he answers at least 12 questions correctly.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong>S = {H, T}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image002.png\" \/>\u00a0= 2<\/p>\n<p style=\"text-align: justify;\">Let A represents a head.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image039.png\" \/>\u00a0A = {H}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image003.png\" \/>\u00a0= 1<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image044.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image045.png\" \/>\u00a0 and\u00a0 P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = <img decoding=\"async\" style=\"height: 25px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (at least 12 success) = P (X = 12) + P (X = 13) + \u2026\u2026\u2026 P (X = 20)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 403px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image046.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 465px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image047.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-5\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_Suppose_X_has_a_binomial_distribution_B_Show_that_X_3_is_the_most_likely_outcome\"><\/span><strong>8.\u00a0 Suppose X has a binomial distribution B<\/strong><strong><img decoding=\"async\" style=\"height: 45px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image048.png\" \/><\/strong><strong>. Show that X = 3 is the most likely outcome.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong>B <img decoding=\"async\" style=\"height: 45px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image048.png\" \/>\u00a0\u00a0\u00a0<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 41px; width: 123px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image049.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image050.png\" \/>\u00a0= 0, 1, 2, 3, 4, 5, 6<\/p>\n<p style=\"text-align: justify;\">P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = C<img decoding=\"async\" style=\"height: 27px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\">Since\u00a0 <img decoding=\"async\" style=\"height: 17px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = C<img decoding=\"async\" style=\"height: 27px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\">Now,\u00a0 out of C (6, 0), C (6, 1), C (6, 2), C (6, 3), C (6, 4), C (6, 5), C (6, 6), here C (6, 3) is maximum.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image039.png\" \/>\u00a0P (X = 3) = C (6, 3) <img decoding=\"async\" style=\"height: 49px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image053.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image054.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 84px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image055.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, P (X = 3) is maximum, i.e., <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image056.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-6\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_On_a_multiple_choice_examination_with_three_possible_answers_for_each_of_the_five_questions_what_is_the_probability_that_a_candidate_would_get_four_or_more_correct_answers_just_by_guessing\"><\/span><strong>9.\u00a0 On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong><img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image057.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 129px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image058.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image059.png\" \/>\u00a0and P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = <img decoding=\"async\" style=\"height: 25px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (Four or more success) = P (X = 4) + P (X = 5)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 165px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image060.png\" \/>= <img decoding=\"async\" style=\"height: 49px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image061.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 31px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image062.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-7\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_A_person_buys_a_lottery_ticket_in_50_lotteries_in_each_of_which_his_chance_of_winning_a_prize_is_What_is_the_probability_that_he_will_win_a_prize\"><\/span><strong>10.\u00a0 A person buys a lottery ticket in 50 lotteries, in each of which his chance of winning a prize is <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image063.png\" \/><\/strong><strong>\u00a0\u00a0What is the probability that he will win a prize:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>(a) at least once\u00a0 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(b) exactly once\u00a0 <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(c) at least twice?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.<\/strong>\u00a0 <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image064.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 160px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image065.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 19px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image066.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(a)<\/strong>\u00a0 P (at least one prize) = 1 \u2013 P (X = 0) = <img decoding=\"async\" style=\"height: 49px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image067.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(b)<\/strong>\u00a0 P (exactly one prize) = P (X = 1) = <img decoding=\"async\" style=\"height: 49px; width: 329px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image068.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(c)<\/strong>\u00a0 P (at least twice) = 1 \u2013 [P (X = 0) + P (X = 1)] = <img decoding=\"async\" style=\"height: 53px; width: 168px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image069.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 272px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image070.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-8\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11_Find_the_probability_of_getting_5_exactly_twice_in_7_throws_of_a_die\"><\/span><strong>11.\u00a0 Find the probability of getting 5 exactly twice in 7 throws of a die.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong>S = {1, 2, 3, 4, 5, 6}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image002.png\" \/>\u00a0= 6<\/p>\n<p style=\"text-align: justify;\">A = {5}\u00a0\u00a0\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image003.png\" \/>\u00a0= 1<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image071.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image072.png\" \/>\u00a0and P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = <img decoding=\"async\" style=\"height: 25px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 2) = <img decoding=\"async\" style=\"height: 49px; width: 273px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image073.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-9\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_Find_the_probability_of_throwing_at_most_2_sixes_in_6_throws_of_a_single_die\"><\/span><strong>12.\u00a0 Find the probability of throwing at most 2 sixes in 6 throws of a single die.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans.<\/strong>\u00a0 S = {1, 2, 3, 4, 5, 6}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image002.png\" \/>\u00a0= 6<\/p>\n<p style=\"text-align: justify;\">Let A represents the favourable event i.e., 6<\/p>\n<p style=\"text-align: justify;\">A = {6}\u00a0 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image003.png\" \/>\u00a0= 1<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 49px; width: 95px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image071.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 99px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image074.png\" \/>\u00a0and P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = <img decoding=\"async\" style=\"height: 25px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 0) = <img decoding=\"async\" style=\"height: 49px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image075.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 1) = <img decoding=\"async\" style=\"height: 49px; width: 136px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image076.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 2) = <img decoding=\"async\" style=\"height: 49px; width: 196px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image077.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (at most 2 success) = P (X = 0) + P (X = 1) + P (X = 2)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image075.png\" \/>\u00a0+ <img decoding=\"async\" style=\"height: 49px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image078.png\" \/>\u00a0+ <img decoding=\"async\" style=\"height: 49px; width: 87px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image079.png\" \/><\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 49px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image080.png\" \/>\u00a0\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image081.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-10\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_It_is_known_that_10_of_certain_articles_manufactured_are_defective_What_is_the_probability_that_in_a_random_sample_of_12_such_articles_9_are_defective\"><\/span><strong>13.\u00a0 It is known that 10% of certain articles manufactured are defective. What is the probability that in a random sample of 12 such articles 9 are defective?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>Ans.<\/strong>\u00a0 <img decoding=\"async\" style=\"height: 41px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image082.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 149px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image083.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image084.png\" \/>\u00a0and P (X = <img decoding=\"async\" style=\"height: 13px; width: 12px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image008.png\" \/>) = <img decoding=\"async\" style=\"height: 25px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 9) = <img decoding=\"async\" style=\"height: 49px; width: 244px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image085.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 68px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image086.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-11\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><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 style=\"text-align: justify;\"><strong>14.\u00a0 Binomial distribution is given this name because:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(A)\u00a0 This distribution was evolved by James binomial.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B)\u00a0 Each trial has only two outcomes. Namely success and failure.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C)\u00a0 Its probability function is obtained by general of binomial expansion.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D)\u00a0 It is obtained by combining two distributions.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong><img decoding=\"async\" style=\"height: 41px; width: 89px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image087.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image041.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image088.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 0) = <img decoding=\"async\" style=\"height: 49px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image089.png\" \/><\/p>\n<p style=\"text-align: justify;\">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_135-12\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"15_In_a_box_containing_100_bulbs_10_are_defective_The_probability_that_out_of_a_sample_of_5_bulbs_none_is_defective_is\"><\/span><strong>15.\u00a0 In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 21px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image090.png\" \/>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 49px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image091.png\" \/>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) <img decoding=\"async\" style=\"height: 49px; width: 43px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image089.png\" \/>\u00a0\u00a0\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image092.png\" \/>\u00a0<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans.\u00a0 <\/strong><img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image093.png\" \/>\u00a0and <img decoding=\"async\" style=\"height: 41px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image094.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image095.png\" \/><\/p>\n<p style=\"text-align: justify;\">P (X = 4) = <img decoding=\"async\" style=\"height: 49px; width: 91px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.5\/image096.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, option (A) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_135-13\"><\/span>NCERT Solutions class 12 Maths Exercise 13.5<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 13.5 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 13.5\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-5\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 13.5\">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-4542","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 13.5 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 13.5 in PDF format for free download. 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