{"id":4540,"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-13-3\/"},"modified":"2018-05-08T11:16:54","modified_gmt":"2018-05-08T05:46:54","slug":"ncert-solutions-class-12-maths-exercise-13-3","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-3\/","title":{"rendered":"NCERT Solutions class 12 Maths Exercise 13.3"},"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-13-3\/#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-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133\" >NCERT Solutions class 12 Maths Exercise 13.3<\/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-13-3\/#6_There_are_three_coins_One_is_a_two_headed_coin_another_is_a_biased_coin_that_comes_up_heads_75_of_the_time_and_third_is_an_unbiased_coin_One_of_the_three_coins_is_chosen_at_random_and_tossed_it_shows_head_what_is_the_probability_that_it_was_the_two_headed_coin\" >6. There are three coins. One is a two headed coin, another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows head, what is the probability that it was the two headed coin?<\/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-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133-2\" >NCERT Solutions class 12 Maths Exercise 13.3<\/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-13-3\/#7_An_insurance_company_insured_2000_scooter_driver_4000_car_drivers_and_6000_truck_drivers_The_probability_of_accidents_are_001_003_and_015_respectively_One_of_the_insured_persons_meets_with_an_accident_What_is_the_probability_that_he_is_a_scooter_driver\" >7. An insurance company insured 2000 scooter driver, 4000 car drivers and 6000 truck drivers. The probability of accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?<\/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-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133-3\" >NCERT Solutions class 12 Maths Exercise 13.3<\/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-13-3\/#8_A_factory_has_two_machines_A_and_B_Past_record_shows_that_machine_A_produced_60_of_the_items_of_output_and_machine_B_produced_40_of_the_items_Further_2_of_the_items_produced_by_machine_A_and_1_produced_by_machine_B_were_defective_All_the_items_are_put_into_one_stockpile_and_then_one_item_is_chosen_at_random_from_this_and_is_found_to_be_defective_What_is_the_probability_that_it_was_produced_by_machine_B\" >8. A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?<\/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-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133-4\" >NCERT Solutions class 12 Maths Exercise 13.3<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-3\/#9_Two_groups_are_competing_for_the_position_on_the_Board_of_directors_of_a_corporation_The_probabilities_that_the_first_and_the_second_groups_will_win_are_06_and_04_respectively_Further_if_the_first_group_wins_the_probability_of_introducing_a_new_product_is_07_and_the_corresponding_probability_if_03_if_the_second_group_wins_Find_the_probability_that_the_new_product_introduced_was_by_the_second_group\" >9. Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability if 0.3, if the second group wins. Find the probability that the new product introduced was by the second group.<\/a><ul class='ez-toc-list-level-4' ><li class='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-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133-5\" >NCERT Solutions class 12 Maths Exercise 13.3<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-3\/#10_Suppose_a_girl_throws_a_die_If_she_gets_a_5_or_6_she_tosses_a_coin_three_times_and_notes_the_number_of_heads_If_she_gets_1_2_3_or_4_she_tosses_a_coin_once_and_noted_whether_a_head_or_tail_is_obtained_If_she_obtained_exactly_one_head_what_is_the_probability_that_she_threw_1_2_3_and_4_with_the_die\" >10. Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4 she tosses a coin once and noted whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 and 4 with the die?<\/a><ul class='ez-toc-list-level-4' ><li class='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-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133-6\" >NCERT Solutions class 12 Maths Exercise 13.3<\/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-13-3\/#11_A_manufacturer_has_three_machine_operators_A_B_and_C_The_first_operator_A_produces_1_defective_items_whereas_the_other_two_operators_B_and_C_produce_5_and_7_defective_items_respectively_A_is_on_the_job_for_50_of_the_time_B_on_the_job_for_30_of_the_time_and_C_on_the_job_for_20_of_the_time_A_defective_item_is_produced_what_is_the_probability_that_it_was_produced_by_A\" >11. A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, whereas the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B on the job for 30% of the time and C on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?<\/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-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133-7\" >NCERT Solutions class 12 Maths Exercise 13.3<\/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-13-3\/#12_A_card_from_a_pack_of_52_cards_is_lost_From_the_remaining_cards_of_the_pack_two_cards_are_drawn_and_are_found_to_be_both_diamonds_Find_the_probability_of_the_lost_card_being_a_diamond\" >12. A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.<\/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-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133-8\" >NCERT Solutions class 12 Maths Exercise 13.3<\/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-13-3\/#13_Probability_that_A_speaks_truth_is_A_coin_is_tossed_A_report_that_a_head_appears_The_probability_that_actually_there_was_head_is\" >13. Probability that A speaks truth is \u00a0A coin is tossed. A report that a head appears. The probability that actually there was head is:<\/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-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133-9\" >NCERT Solutions class 12 Maths Exercise 13.3<\/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-13-3\/#14_If_A_and_B_are_two_events_such_that_A_B_and_P_B_0_then_which_of_the_following_is_correct\" >14. If A and B are two events such that A \u00a0B and P (B) \u00a00, then which of the following is correct:<\/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-20\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-3\/#NCERT_Solutions_class_12_Maths_Exercise_133-10\" >NCERT Solutions class 12 Maths Exercise 13.3<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-3\/#CBSE_App_for_Students\" >CBSE App for Students<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions class 12 Maths Exercise 13.3 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 13.3\" width=\"188\" height=\"241\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Probability\"><\/span>NCERT Solutions class 12 Maths Probability<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. An urn contains 5 red and 5 black balls. A ball is drawn at random, its colour is noted and is returned to the urn. Moreover, 2 additional balls of the colour drawn are put in the urn and then a ball is drawn at random. What is the probability that the second ball is red?<\/strong><\/p>\n<p><strong>Ans. Case (i) :<\/strong> S<sub>1<\/sub> = {5 red balls, 5 black balls}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image002.png\" \/>\u00a0= 10<\/p>\n<p>Let us draw a red balls first, i.e., A<sub>1<\/sub> = {5 red balls}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image003.png\" \/>\u00a0= 5<\/p>\n<p>P (A<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 49px; width: 107px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image004.png\" \/><\/p>\n<p>Now after adding 2 balls of the same colour, i.e.,<\/p>\n<p>S<sub>2<\/sub> = {7 red balls, 5 black balls}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image005.png\" \/>\u00a0= 12<\/p>\n<p>Let us draw a red balls first, i.e., A<sub>2<\/sub> = {7 red balls}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image006.png\" \/>\u00a0= 7<\/p>\n<p>P (A<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 49px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image007.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image008.png\" \/>\u00a0\u00a0P (a red ball is drawn) = <img decoding=\"async\" style=\"height: 41px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image009.png\" \/><\/p>\n<p>Case (ii) : When a black ball is drawn, i.e., A<sub>2<\/sub> = {5 red balls}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image006.png\" \/>\u00a0= 5<\/p>\n<p>P (A<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 49px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image010.png\" \/><\/p>\n<p>Now after adding 2 balls of the same colour, i.e.,<\/p>\n<p>S<sub>2<\/sub> = {5 red balls, 7 black balls}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 27px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image005.png\" \/>\u00a0= 12<\/p>\n<p>Let us draw a red balls first, i.e., A<sub>2<\/sub> = {5 red balls}<\/p>\n<p><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 27px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image006.png\" \/>\u00a0= 5<\/p>\n<p>P (A<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 49px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image011.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image012.png\" \/>\u00a0\u00a0P (a red ball is drawn) = <img decoding=\"async\" style=\"height: 41px; width: 79px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image013.png\" \/><\/p>\n<p>Therefore, required probability in both cases = <img decoding=\"async\" style=\"height: 41px; width: 117px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image014.png\" \/><\/p>\n<hr \/>\n<p><strong>2. A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.<\/strong><\/p>\n<p><strong>Ans.<\/strong> Let A be the event hat ball drawn is red and let E1 and E2 be the events that the ball drawn is from the first bag and second bag respectively.<\/p>\n<p>P (E<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image015.png\" \/>, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image015.png\" \/>,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>\u00a0= P (drawing a red ball from bag I) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image017.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>\u00a0= P (drawing a red ball from bag II) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image019.png\" \/><\/p>\n<p>Therefore, by Bayes\u2019 theorem,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image020.png\" \/>\u00a0= P (red ball drawn from bag I) = <img decoding=\"async\" style=\"height: 54px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image021.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 80px; width: 216px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image022.png\" \/><\/p>\n<hr \/>\n<p><strong>3. Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostler?<\/strong><\/p>\n<p><strong>Ans.<\/strong> Let E<sub>1<\/sub> = the examinee knows the answer, E<sub>2<\/sub> = the examinee guesses the answer and<\/p>\n<p>A = student who attain grade A, P (E<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image023.png\" \/>, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image024.png\" \/>,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image025.png\" \/>\u00a0P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image026.png\" \/><\/p>\n<p>Therefore, by Bayes\u2019 theorem,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image021.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 80px; width: 315px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image027.png\" \/><\/p>\n<hr \/>\n<p><strong>4. In answering a question on a multiple choice test a student either knows the answer or guesses. Let <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image028.png\" \/><\/strong><strong>\u00a0be the probability that he knows the answer and <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image029.png\" \/><\/strong><strong>\u00a0be the probability that he guesses. Assuming that a student who guesses the answer, will be correct with probability <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image029.png\" \/><\/strong><strong>. What is the probability that a student knows the answer given that he answered it correctly?<\/strong><\/p>\n<p><strong>Ans.<\/strong> Let E<sub>1<\/sub> = students residing in the hostel, E<sub>2<\/sub> = day scholars (not residing in the hostel) and<\/p>\n<p>A = the examinee answers correctly<\/p>\n<p>Now P (E<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image028.png\" \/>, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image029.png\" \/>,<\/p>\n<p>Since E<sub>1<\/sub> and E<sub>2<\/sub> are mutually exclusive events and exhaustive events, and if E<sub>2<\/sub> has already occurred, then the examinee guesses, therefore the probability that he answers correctly given that he has made a guess is <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image029.png\" \/>\u00a0i.e., P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image029.png\" \/><\/p>\n<p>And P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>\u00a0= P (answers correctly given that he knew the answer) = 1<\/p>\n<p>Therefore, by Bayes\u2019 theorem,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image021.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 80px; width: 211px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image030.png\" \/><\/p>\n<hr \/>\n<p><strong>5. A laboratory blood test is 99% effective in detecting a certain disease when it is, in fact, present. However, the test also yields a false positive result for 0.5% of the healthy person tested (i.e., if a healthy person is tested, then, with probability 0.005, the test will imply he has the disease). If 0.1 percent of the population actually has the disease, what is the probability that a person has the disease given that his test result is positive?<\/strong><\/p>\n<p><strong>Ans.<\/strong> \u00a0Let E<sub>1<\/sub> = The person selected is suffering from certain disease, E<sub>2<\/sub> = The person selected is not suffering from certain disease and A = The doctor diagnoses correctly<\/p>\n<p>Now P (E<sub>1<\/sub>) = 0.1% = <img decoding=\"async\" style=\"height: 41px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image031.png\" \/>\u00a0= 0.001, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 157px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image032.png\" \/>,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>\u00a0= 99% = <img decoding=\"async\" style=\"height: 41px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image033.png\" \/>\u00a0P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>\u00a0= 0.005%<\/p>\n<p>Therefore, by Bayes\u2019 theorem,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image021.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 300px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image034.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"6_There_are_three_coins_One_is_a_two_headed_coin_another_is_a_biased_coin_that_comes_up_heads_75_of_the_time_and_third_is_an_unbiased_coin_One_of_the_three_coins_is_chosen_at_random_and_tossed_it_shows_head_what_is_the_probability_that_it_was_the_two_headed_coin\"><\/span><strong>6. There are three coins. One is a two headed coin, another is a biased coin that comes up heads 75% of the time and third is an unbiased coin. One of the three coins is chosen at random and tossed, it shows head, what is the probability that it was the two headed coin?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> Let E<sub>1<\/sub> = a two headed coin, E<sub>2<\/sub> = a biased coin, E<sub>3<\/sub> = an unbiased coin and A = A head is shown<\/p>\n<p>Now P (E<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image035.png\" \/>, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image035.png\" \/>, P (E<sub>3<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image035.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>\u00a0= 1, P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image036.png\" \/>\u00a0and\u00a0 P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image037.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image015.png\" \/><\/p>\n<p>Therefore, by Bayes\u2019 theorem,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 331px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image038.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 80px; width: 297px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image039.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133-2\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"7_An_insurance_company_insured_2000_scooter_driver_4000_car_drivers_and_6000_truck_drivers_The_probability_of_accidents_are_001_003_and_015_respectively_One_of_the_insured_persons_meets_with_an_accident_What_is_the_probability_that_he_is_a_scooter_driver\"><\/span><strong>7. An insurance company insured 2000 scooter driver, 4000 car drivers and 6000 truck drivers. The probability of accidents are 0.01, 0.03 and 0.15 respectively. One of the insured persons meets with an accident. What is the probability that he is a scooter driver?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> Let E<sub>1<\/sub> = Person chosen is a scooter driver, E<sub>2<\/sub> = Person chosen is a car driver, E<sub>3<\/sub> = Person chosen is a truck driver and A = Person meets with an accident<\/p>\n<p>Since there are 12000 persons, therefore,<\/p>\n<p>Now P (E<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image040.png\" \/>, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 71px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image041.png\" \/>, P (E<sub>3<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image042.png\" \/><\/p>\n<p>It is given that P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>= P (a person meets with an accident, he is a scooter driver) = 0.01<\/p>\n<p>Similarly, P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>\u00a0= 0.03 and\u00a0 P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image037.png\" \/>\u00a0= 0.15<\/p>\n<p>To find: P (person meets with an accident that he was a scooter driver)<\/p>\n<p>Therefore, by Bayes\u2019 theorem,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 331px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image038.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 80px; width: 294px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image043.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133-3\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"8_A_factory_has_two_machines_A_and_B_Past_record_shows_that_machine_A_produced_60_of_the_items_of_output_and_machine_B_produced_40_of_the_items_Further_2_of_the_items_produced_by_machine_A_and_1_produced_by_machine_B_were_defective_All_the_items_are_put_into_one_stockpile_and_then_one_item_is_chosen_at_random_from_this_and_is_found_to_be_defective_What_is_the_probability_that_it_was_produced_by_machine_B\"><\/span><strong>8. A factory has two machines A and B. Past record shows that machine A produced 60% of the items of output and machine B produced 40% of the items. Further, 2% of the items produced by machine A and 1% produced by machine B were defective. All the items are put into one stockpile and then one item is chosen at random from this and is found to be defective. What is the probability that it was produced by machine B?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> Given: P (A) = <img decoding=\"async\" style=\"height: 41px; width: 35px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image044.png\" \/>\u00a0P (B) = <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image024.png\" \/><\/p>\n<p>Let D denotes a defective item:<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image008.png\" \/>\u00a0\u00a0P<img decoding=\"async\" style=\"height: 30px; width: 45px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image045.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image046.png\" \/>\u00a0and P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image047.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image048.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image049.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 197px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image050.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 80px; width: 283px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image051.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133-4\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h3><span class=\"ez-toc-section\" id=\"9_Two_groups_are_competing_for_the_position_on_the_Board_of_directors_of_a_corporation_The_probabilities_that_the_first_and_the_second_groups_will_win_are_06_and_04_respectively_Further_if_the_first_group_wins_the_probability_of_introducing_a_new_product_is_07_and_the_corresponding_probability_if_03_if_the_second_group_wins_Find_the_probability_that_the_new_product_introduced_was_by_the_second_group\"><\/span><strong>9. Two groups are competing for the position on the Board of directors of a corporation. The probabilities that the first and the second groups will win are 0.6 and 0.4 respectively. Further, if the first group wins, the probability of introducing a new product is 0.7 and the corresponding probability if 0.3, if the second group wins. Find the probability that the new product introduced was by the second group.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans.<\/strong> Given: P (G1) = 0.6, P (G2) = 0.4<\/p>\n<p>Let P denotes the launching of new product.<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image008.png\" \/>\u00a0\u00a0P (P<strong>\u0964<\/strong>G<sub>1<\/sub>) = 0.7, P (P<strong>\u0964<\/strong>G<sub>2<\/sub>) = 0.3<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image052.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 219px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image053.png\" \/>= <img decoding=\"async\" style=\"height: 41px; width: 186px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image054.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133-5\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h3><span class=\"ez-toc-section\" id=\"10_Suppose_a_girl_throws_a_die_If_she_gets_a_5_or_6_she_tosses_a_coin_three_times_and_notes_the_number_of_heads_If_she_gets_1_2_3_or_4_she_tosses_a_coin_once_and_noted_whether_a_head_or_tail_is_obtained_If_she_obtained_exactly_one_head_what_is_the_probability_that_she_threw_1_2_3_and_4_with_the_die\"><\/span><strong>10. Suppose a girl throws a die. If she gets a 5 or 6, she tosses a coin three times and notes the number of heads. If she gets 1, 2, 3 or 4 she tosses a coin once and noted whether a head or tail is obtained. If she obtained exactly one head, what is the probability that she threw 1, 2, 3 and 4 with the die?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ans.<\/strong> Let E<sub>1<\/sub> = 5 or 6 appears on a die, E<sub>2<\/sub> = 1, 2, 3 or 4 appears on a die and A = A head appears on the coin.<\/p>\n<p>Now P (E<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image055.png\" \/>, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image056.png\" \/><\/p>\n<p>Now P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>\u00a0Probability of getting a head on tossing a coin three times,<\/p>\n<p>when E<sub>1<\/sub> has already occurs = P (HTT) or P (THT) or P (TTH)<\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 203px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image057.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image058.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>\u00a0= Probability of getting a head on tossing a coin once,<\/p>\n<p>when E<sub>2<\/sub> has already occurred = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image015.png\" \/><\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image008.png\" \/>\u00a0\u00a0P (there is exactly one head given that 1, 2, 3 or 4 appears on a die)<\/p>\n<p>&nbsp;<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image059.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image060.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 80px; width: 222px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image061.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133-6\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"11_A_manufacturer_has_three_machine_operators_A_B_and_C_The_first_operator_A_produces_1_defective_items_whereas_the_other_two_operators_B_and_C_produce_5_and_7_defective_items_respectively_A_is_on_the_job_for_50_of_the_time_B_on_the_job_for_30_of_the_time_and_C_on_the_job_for_20_of_the_time_A_defective_item_is_produced_what_is_the_probability_that_it_was_produced_by_A\"><\/span><strong>11. A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, whereas the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B on the job for 30% of the time and C on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> Let E<sub>1<\/sub> = the item is manufactured by the operator A, E<sub>2<\/sub> = the item is manufactured by the operator B, E<sub>3<\/sub> = the item is manufactured by the operator C and A = the item is defective<\/p>\n<p>Now P (E<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image062.png\" \/>, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image063.png\" \/>, P (E<sub>3<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image026.png\" \/><\/p>\n<p>Now P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>= P (item drawn is manufactured by operator A) = <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image048.png\" \/><\/p>\n<p>Similarly, P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image064.png\" \/>\u00a0\u00a0and\u00a0 P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image037.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 41px; width: 30px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image065.png\" \/><\/p>\n<p>Now Required probability = Probability that the item is manufactured by operator A given that the item drawn is defective<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 331px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image038.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 80px; width: 357px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image066.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133-7\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"12_A_card_from_a_pack_of_52_cards_is_lost_From_the_remaining_cards_of_the_pack_two_cards_are_drawn_and_are_found_to_be_both_diamonds_Find_the_probability_of_the_lost_card_being_a_diamond\"><\/span><strong>12. A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>Ans.<\/strong> Let E<sub>1<\/sub> = the missing card is a diamond, E<sub>2<\/sub> = the missing card is a spade, E<sub>3<\/sub> = the missing card is a club, E<sub>4<\/sub> = the missing card is a heart and A = drawing of two heart cards from the remaining cards.<\/p>\n<p>Now P (E<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image067.png\" \/>, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image067.png\" \/>, P (E<sub>3<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image067.png\" \/>, P (E<sub>4<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image067.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>= P (drawing 2 heart cards given that one diamond card is missing) = <img decoding=\"async\" style=\"height: 49px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image068.png\" \/><\/p>\n<p>Similarly, P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image069.png\" \/>, P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image037.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image069.png\" \/>\u00a0\u00a0and P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image070.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image069.png\" \/><\/p>\n<p>By Bayes\u2019 theorem,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 444px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image071.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 96px; width: 363px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image072.png\" \/><\/p>\n<p>= <img decoding=\"async\" style=\"height: 41px; width: 159px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image073.png\" \/><\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133-8\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"13_Probability_that_A_speaks_truth_is_A_coin_is_tossed_A_report_that_a_head_appears_The_probability_that_actually_there_was_head_is\"><\/span><strong>13. Probability that A speaks truth is <\/strong><strong><img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image074.png\" \/><\/strong><strong>\u00a0A coin is tossed. A report that a head appears. The probability that actually there was head is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(A) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image075.png\" \/>\u00a0\u00a0<\/strong><\/p>\n<p><strong>(B) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image015.png\" \/>\u00a0\u00a0<\/strong><\/p>\n<p><strong>(C) <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image076.png\" \/>\u00a0\u00a0<\/strong><\/p>\n<p><strong>(D) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image077.png\" \/>\u00a0<\/strong><\/p>\n<p><strong>Ans. <\/strong>Let A be the event that the man reports that head occurs in tossing a coin and let E<sub>1<\/sub> be the event that head occurs and E<sub>2<\/sub> be the event head does not occur.<\/p>\n<p>P (E<sub>1<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image015.png\" \/>, P (E<sub>2<\/sub>) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image015.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image016.png\" \/>= P (A reports that head occurs when head had actually occur red on the coin) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image075.png\" \/><\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image018.png\" \/>= P (A reports that head occurs when head had not occur red on the coin) = <img decoding=\"async\" style=\"height: 41px; width: 60px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image078.png\" \/><\/p>\n<p>By Bayes\u2019 theorem,<\/p>\n<p>P<img decoding=\"async\" style=\"height: 30px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image020.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 54px; width: 217px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image021.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 80px; width: 161px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image079.png\" \/><\/p>\n<p>Hence, option (A) is correct.<\/p>\n<hr \/>\n<h4 style=\"text-align: center;\"><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133-9\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<h4><span class=\"ez-toc-section\" id=\"14_If_A_and_B_are_two_events_such_that_A_B_and_P_B_0_then_which_of_the_following_is_correct\"><\/span><strong>14. If A and B are two events such that A <\/strong><strong><img decoding=\"async\" style=\"height: 13px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image080.png\" \/><\/strong><strong>\u00a0B and P (B) <\/strong><strong><img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image081.png\" \/><\/strong><strong>\u00a00, then which of the following is correct:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p><strong>(A) P<\/strong><strong><img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image082.png\" \/><\/strong><strong> = <\/strong><strong><img decoding=\"async\" style=\"height: 44px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image083.png\" \/><\/strong><strong>\u00a0<\/strong><\/p>\n<p><strong>(B) P<\/strong><strong><img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image082.png\" \/><\/strong><strong> &lt; P (A)<\/strong><\/p>\n<p><strong>(C) P <\/strong><strong><img decoding=\"async\" style=\"height: 30px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image084.png\" \/><\/strong><strong>\u00a0P (A)<\/strong><\/p>\n<p><strong>(D) None of these<\/strong><\/p>\n<p><strong>Ans. <\/strong>A <img decoding=\"async\" style=\"height: 13px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image080.png\" \/>\u00a0B <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0\u00a0A <img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image085.png\" \/>\u00a0B = A P \u00a0and P (B) <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image081.png\" \/>\u00a00 <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image082.png\" \/>\u00a0= <img decoding=\"async\" style=\"height: 49px; width: 125px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image086.png\" \/><\/p>\n<p>Since P (B) <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image081.png\" \/>\u00a00<\/p>\n<p><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image008.png\" \/>\u00a0\u00a0<img decoding=\"async\" style=\"height: 49px; width: 42px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image087.png\" \/>\u00a0&lt; 1<img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0P (A) &lt; P (B) <img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image001.png\" \/>\u00a0P<img decoding=\"async\" style=\"height: 30px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image082.png\" \/>\u00a0<img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/12\/maths\/Ex13.3\/image088.png\" \/>\u00a0P (A)<\/p>\n<p>Hence, option (C) is correct.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_class_12_Maths_Exercise_133-10\"><\/span>NCERT Solutions class 12 Maths Exercise 13.3<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 13.3 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 13.3\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-12-maths-exercise-13-3\/\" aria-label=\"More on NCERT Solutions class 12 Maths Exercise 13.3\">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-4540","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 13.3 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions class 12 Maths Exercise 13.3 in PDF format for free download. 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