{"id":4942,"date":"2016-05-19T09:49:00","date_gmt":"2016-05-19T04:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-10-maths-exercise-15-1\/"},"modified":"2023-03-22T15:19:57","modified_gmt":"2023-03-22T09:49:57","slug":"ncert-solutions-for-class-10-maths-exercise-15-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/","title":{"rendered":"NCERT Solutions for Class 10 Maths Exercise 15.1"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#NCERT_Solutions_for_Class_10_Maths_Probability\" >NCERT Solutions for Class 10 Maths\u00a0Probability<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#1_Complete_the_statements\" >1. Complete the statements:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#2_Which_of_the_following_experiments_have_equally_likely_outcomes_Explain\" >2. Which of the following experiments have equally likely outcomes? Explain.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#3_Why_is_tossing_a_coin_considered_to_be_a_fair_way_of_deciding_which_team_should_get_the_ball_at_the_beginning_of_a_football_game\" >3. Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#4_Which_of_the_following_cannot_be_the_probability_of_an_event\" >4. Which of the following cannot be the probability of an event:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#5_If_PE_005_what_is_the_probability_of_%E2%80%98not_E\" >5. If P(E) = 0.05, what is the probability of \u2018not E\u2019?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#6_A_bag_contains_lemon_flavoured_candles_only_Malini_takes_out_one_candy_without_looking_into_the_bag_What_is_the_probability_that_she_takes_out\" >6. A bag contains lemon flavoured candles only. Malini takes out one candy without looking into the bag. What is the probability that she takes out:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#7_It_is_given_that_in_a_group_of_3_students_the_probability_of_2_students_not_having_the_same_birthday_is_0992_What_is_the_probability_that_the_2_students_have_the_same_birthday\" >7. It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#8_A_bag_contains_3_red_balls_and_5_black_balls_A_ball_is_drawn_at_random_from_the_bag_What_is_the_probability_that_the_ball_drawn_is\" >8. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#9_A_box_contains_5_red_marbles_8_white_marbles_and_4_green_marbles_One_marble_is_taken_out_of_the_box_at_random_What_is_the_probability_that_the_marble_taken_out_will_be\" >9. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#10_A_piggy_bank_contains_hundred_50_p_coins_fifty_Re_1_coins_twenty_Rs_2coins_and_ten_Rs_5_coins_If_it_is_equally_likely_that_of_the_coins_will_fall_out_when_the_bank_is_turned_upside_down_what_is_the_probability_that_the_coin\" >10. A piggy bank contains hundred 50 p coins, fifty Re. 1 coins, twenty Rs. 2coins and ten Rs. 5 coins. If it is equally likely that of the coins will fall out when the bank is turned upside down, what is the probability that the coin:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#11_Gopi_buys_a_fish_from_a_shop_for_his_aquarium_The_shopkeeper_takes_out_one_fish_at_random_from_a_tank_containing_5_male_fishes_and_8_female_fishes_see_figure_What_is_the_probability_that_the_fish_taken_out_is_a_male_fish\" >11. Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fishes and 8 female fishes (see figure). What is the probability that the fish taken out is a male fish?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#12_A_game_of_chance_consists_of_spinning_an_arrow_which_comes_to_rest_pointing_at_one_of_the_numbers_1_2_3_4_5_6_7_8_see_figure_and_these_are_equally_likely_outcomes_What_is_the_probability_that_it_will_point_at\" >12. A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#13_A_dice_is_thrown_once_Find_the_probability_of_getting\" >13. A dice is thrown once. Find the probability of getting:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#14_One_card_is_drawn_from_a_well-shuffled_deck_of_52_cards_Find_the_probability_of_getting\" >14. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#15_Five_cards_%E2%80%93_then_ten_jack_queen_king_and_ace_of_diamonds_are_well-shuffled_with_their_face_downwards_One_card_is_then_picked_up_at_random\" >15. Five cards \u2013 then ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#16_12_defective_pens_are_accidently_mixed_with_132_good_ones_It_is_not_possible_to_just_look_at_a_pen_and_tell_whether_or_not_it_is_defective_One_pen_is_taken_out_at_random_from_this_lot_Determine_the_probability_that_the_pen_taken_out_is_a_good_one\" >16. 12 defective pens are accidently mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#17_i_A_lot_of_20_bulbs_contains_4_defective_ones_One_bulb_is_drawn_at_random_from_the_lot_What_is_the_probability_that_this_bulb_is_defective\" >17. (i) A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#18_A_box_contains_90_discs_which_are_numbered_from_1_to_90_If_one_disc_is_drawn_at_random_from_the_box_find_the_probability_that_it_bears_i_a_two-digit_number_ii_a_perfect_square_number_iii_a_number_divisible_by_5\" >18. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#19_A_child_has_a_die_whose_six_faces_show_the_letters_as_given_below\" >19. A child has a die whose six faces show the letters as given below:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#20_Suppose_you_drop_a_die_at_random_on_the_rectangular_region_shown_in_the_figure_given_on_the_next_page_What_is_the_probability_that_it_will_land_inside_the_circle_with_diameter_1_m\" >20. Suppose you drop a die at random on the rectangular region shown in the figure given on the next page. What is the probability that it will land inside the circle with diameter 1 m?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#21_A_lot_consists_of_144_ball_pens_of_which_20_are_defective_and_the_others_are_good_Nuri_will_buy_a_pen_if_it_is_good_but_will_not_buy_if_it_is_defective_The_shopkeeper_draws_one_pen_at_random_and_gives_it_to_her_What_is_the_probability_that\" >21. A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#22_Refer_to_example_13\" >22. Refer to example 13.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#23_A_game_consists_of_tossing_a_one_rupee_coin_3_times_and_noting_its_outcome_each_time_Hanif_wins_if_all_the_tosses_give_the_same_result_ie_three_heads_or_three_tails_and_loses_otherwise_Calculate_the_probability_that_Hanif_will_lose_the_game\" >23. A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#24_A_die_is_thrown_twice_What_is_the_probability_that\" >24. A die is thrown twice. What is the probability that:&amp;<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#25_Which_of_the_following_arguments_are_correct_and_which_are_not_correct_Give_reasons_for_your_answer\" >25. Which of the following arguments are correct and which are not correct? Give reasons for your answer:<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/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-for-class-10-maths-exercise-15-1\/#NCERT_Solutions_for_Class_10_Maths_Exercise_151\" >NCERT Solutions for Class 10 Maths Exercise 15.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-10-maths-exercise-15-1\/#CBSE_app_for_Class_10\" >CBSE app for Class 10<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 10 Maths Exercise 15.1 Class 10 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 10 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>NCERT solutions for Maths\u00a0<\/strong><strong>Probability\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-10-mathematics-statistics\/1214\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/10%20Maths%20Book.jpg\" alt=\"NCERT Solutions for Class 10 Maths Exercise 15.1\" width=\"181\" height=\"223\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Probability\"><\/span>NCERT Solutions for Class 10 Maths\u00a0Probability<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_Complete_the_statements\"><\/span><strong>1. Complete the statements:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) Probability of event E + Probability of event \u201cnot E\u201d = _______________<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) The probability of an event that cannot happen is _______________. Such an event is called _______________.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) The probability of an event that is certain to happen is _______________. Such an event is called _______________.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) The sum of the probabilities of all the elementary events of an experiment is _______________.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) The probability of an event is greater than or equal to _______________ and less than or equal to _______________.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> 1<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> 0, impossible event<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> 1, sure or certain event<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> 1<\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> 0, 1<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_Which_of_the_following_experiments_have_equally_likely_outcomes_Explain\"><\/span><strong>2. Which of the following experiments have equally likely outcomes? Explain.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) A driver attempts to start a car. The car starts or does not start.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) A player attempts to shoot a basketball. She\/he shoots or misses the shot.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) A trial is made to answer a true-false question. The answer is right or wrong.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) A baby is born. It is a boy or a girl.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> In the experiment, \u201cA driver attempts to start a car. The car starts or does not start\u201d, we are not justified to assume that each outcome is as likely to occur as the other. Thus, the experiment has no equally likely outcomes.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> In the experiment, \u201cA player attempts to shoot a basketball. She\/he shoots or misses the shot\u201d, we are not justified to assume that each outcome is as likely to occur as the other. Thus, the experiment has no equally likely outcomes.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> In the experiment \u201cA trial is made to answer a true-false question. The answer is right or wrong.\u201d We know, in advance, that the result can lead in one of the two possible ways \u2013 either right or wrong. We can reasonably assume that each outcome, right or wrong, is likely to occur as the other. Thus, the outcomes right or wrong are equally likely.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> In the experiment, \u201cA baby is born, It is a boy or a girl\u201d. We know, in advance that the outcome can lead in one of the two possible outcomes \u2013 either a boy or a girl. We are justified to assume that each outcome, boy or girl, is likely to occur as the other. Thus, the outcomes boy or girl are equally likely.<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Why_is_tossing_a_coin_considered_to_be_a_fair_way_of_deciding_which_team_should_get_the_ball_at_the_beginning_of_a_football_game\"><\/span><strong>3. Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>The tossing of a coin is considered to be a fair way of deciding which team should get the ball at the beginning of a football game as we know that the tossing of the coin only land in one of two possible ways \u2013 either head up or tail up. It can reasonably be assumed that each outcome, head or tail, is as likely to occur as the other, i.e., the outcomes head and tail are equally likely. So the result of the tossing of a coin is completely unpredictable.<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Which_of_the_following_cannot_be_the_probability_of_an_event\"><\/span><strong>4. Which of the following cannot be the probability of an event:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(A) <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image001.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(B) <img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image002.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(C) 15% <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(D) 0.7<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (B)<\/strong> Since the probability of an event E is a number P(E) such that<\/p>\n<p style=\"text-align: justify;\">0 <img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image003.png\" \/> P(E) <img decoding=\"async\" style=\"height: 16px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image003.png\" \/> 1<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/><img decoding=\"async\" style=\"height: 19px; width: 33px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image002.png\" \/> cannot be the probability of an event.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_If_PE_005_what_is_the_probability_of_%E2%80%98not_E\"><\/span><strong>5. If P(E) = 0.05, what is the probability of \u2018not E\u2019?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Since P(E) + P (not E) = 1<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>P (not E) = 1 \u2013 P(E) = 1 \u2013 0.05 = 0.95<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_A_bag_contains_lemon_flavoured_candles_only_Malini_takes_out_one_candy_without_looking_into_the_bag_What_is_the_probability_that_she_takes_out\"><\/span><strong>6. A bag contains lemon flavoured candles only. Malini takes out one candy without looking into the bag. What is the probability that she takes out:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) an orange flavoured candy?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) a lemon flavoured candy?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Consider the event related to the experiment of taking out of an orange flavoured candy from a bag containing only lemon flavoured candies. Since no outcome gives an orange flavoured candy, therefore, it is an impossible event so its probability is 0.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Consider the event of taking a lemon flavoured candy out of a bag containing only lemon flavoured candies. This event is a certain event so its probability is 1.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_It_is_given_that_in_a_group_of_3_students_the_probability_of_2_students_not_having_the_same_birthday_is_0992_What_is_the_probability_that_the_2_students_have_the_same_birthday\"><\/span><strong>7. It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let E be the event of having the same birthday<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image005.png\" \/> P(E) = 0.992<\/p>\n<p style=\"text-align: justify;\">But P(E) + P<img decoding=\"async\" style=\"height: 32px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image006.png\" \/> = 1<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> P<img decoding=\"async\" style=\"height: 32px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image006.png\" \/> = 1 \u2013 P(E) = 1 \u2013 0.992 = 0.008<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_A_bag_contains_3_red_balls_and_5_black_balls_A_ball_is_drawn_at_random_from_the_bag_What_is_the_probability_that_the_ball_drawn_is\"><\/span><strong>8. A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) red? <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) not red?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>There are 3 + 5 = 8 balls in a bag. Out of these 8 balls, one can be chosen in 8 ways.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Total number of elementary events = 8<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>Since the bag contains 3 red balls, therefore, one red ball can be drawn in 3 ways.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable number of elementary events = 3<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a red ball) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>Since the bag contains 5 black balls along with 3 red balls, therefore one black (not red) ball can be drawn in 5 ways.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable number of elementary events = 5<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a black ball) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image008.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_A_box_contains_5_red_marbles_8_white_marbles_and_4_green_marbles_One_marble_is_taken_out_of_the_box_at_random_What_is_the_probability_that_the_marble_taken_out_will_be\"><\/span><strong>9. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) red? <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) white? <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) not green?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of marbles in the box = 5 + 8 + 4 = 17<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Total number of elementary events = 17<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>There are 5 red marbles in the box.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable number of elementary events = 5<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> P (getting a red marble) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>There are 8 white marbles in the box.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable number of elementary events = 8<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> P (getting a white marble) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image010.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong>There are 5 + 8 = 13 marbles in the box, which are not green.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable number of elementary events = 13<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> P (not getting a green marble) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image011.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_A_piggy_bank_contains_hundred_50_p_coins_fifty_Re_1_coins_twenty_Rs_2coins_and_ten_Rs_5_coins_If_it_is_equally_likely_that_of_the_coins_will_fall_out_when_the_bank_is_turned_upside_down_what_is_the_probability_that_the_coin\"><\/span><strong>10. A piggy bank contains hundred 50 p coins, fifty Re. 1 coins, twenty Rs. 2coins and ten Rs. 5 coins. If it is equally likely that of the coins will fall out when the bank is turned upside down, what is the probability that the coin:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) will be a 50 p coin?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) will not be a Rs.5 coin?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of coins in a piggy bank = 100 + 50 + 20 + 10 = 180<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Total number of elementary events = 180<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>There are one hundred 50 coins in the piggy bank.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable number of elementary events = 100<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> P (falling out of a 50 p coin) = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image012.png\" \/> = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>There are 100 + 50 + 20 = 170 coins other than Rs. 5 coin.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable number of elementary events = 170<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> P (falling out of a coin other than Rs. 5 coin) = <img decoding=\"async\" style=\"height: 41px; width: 29px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image014.png\" \/> = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image015.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11_Gopi_buys_a_fish_from_a_shop_for_his_aquarium_The_shopkeeper_takes_out_one_fish_at_random_from_a_tank_containing_5_male_fishes_and_8_female_fishes_see_figure_What_is_the_probability_that_the_fish_taken_out_is_a_male_fish\"><\/span><strong>11. Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fishes and 8 female fishes (see figure). What is the probability that the fish taken out is a male fish?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1\" style=\"height: 121px; width: 150px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image016.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of fish in the tank = 5 + 8 = 13<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Total number of elementary events = 13<\/p>\n<p style=\"text-align: justify;\">There are 5 male fishes in the tank.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable number of elementary events = 5<\/p>\n<p style=\"text-align: justify;\">Hence, P (taking out a male fish) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image017.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_A_game_of_chance_consists_of_spinning_an_arrow_which_comes_to_rest_pointing_at_one_of_the_numbers_1_2_3_4_5_6_7_8_see_figure_and_these_are_equally_likely_outcomes_What_is_the_probability_that_it_will_point_at\"><\/span><strong>12. A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 (see figure) and these are equally likely outcomes. What is the probability that it will point at:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 5\" style=\"height: 143px; width: 140px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image018.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i) 8? <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) an odd number?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) a number greater than 2? <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) a number less than 9?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Out of 8 numbers, an arrow can point any of the numbers in 8 ways.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Total number of favourable outcomes = 8<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>Favourable number of outcomes = 1<\/p>\n<p style=\"text-align: justify;\">Hence, P (arrow points at 8) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>Favourable number of outcomes = 4<\/p>\n<p style=\"text-align: justify;\">Hence, P (arrow points at an odd number) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image020.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong>Favourable number of outcomes = 6<\/p>\n<p style=\"text-align: justify;\">Hence, P (arrow points at a number &gt; 2) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image021.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <\/strong>Favourable number of outcomes = 8<\/p>\n<p style=\"text-align: justify;\">Hence, P (arrow points at a number &lt; 9) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image022.png\" \/> =1<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_A_dice_is_thrown_once_Find_the_probability_of_getting\"><\/span><strong>13. A dice is thrown once. Find the probability of getting:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) a prime number.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) a number lying between 2 and 6.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) an odd number.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of favourable outcomes of throwing a dice = 6<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>On a dice, the prime numbers are 2, 3 and 5.<\/p>\n<p style=\"text-align: justify;\">Therefore, favourable outcomes = 3<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a prime number) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image023.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>On a dice, the number lying between 2 and 6 are 3, 4, 5.<\/p>\n<p style=\"text-align: justify;\">Therefore, favourable outcomes = 3<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a number lying between 2 and 6) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image023.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong>On a dice, the odd numbers are 1, 3 and 5.<\/p>\n<p style=\"text-align: justify;\">Therefore, favourable outcomes = 3<\/p>\n<p style=\"text-align: justify;\">Hence P (getting an odd number) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image023.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"14_One_card_is_drawn_from_a_well-shuffled_deck_of_52_cards_Find_the_probability_of_getting\"><\/span><strong>14. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) a king of red colour <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) a face card<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) a red face card <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) the jack of hearts<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) a spade <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(vi) the queen of diamonds.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of favourable outcomes = 52<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>There are two suits of red cards, i.e., diamond and heart. Each suit contains one king.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcomes = 1<\/p>\n<p style=\"text-align: justify;\">Hence, P (a king of red colour) = <img decoding=\"async\" style=\"height: 41px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image024.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>There are 12 face cards in a pack.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcomes = 12<\/p>\n<p style=\"text-align: justify;\">Hence, P (a face card) = <img decoding=\"async\" style=\"height: 41px; width: 55px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image025.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong>There are two suits of red cards, i.e., diamond and heart. Each suit contains 3 face cards.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcomes = <img decoding=\"async\" style=\"height: 19px; width: 32px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image026.png\" \/>= 6<\/p>\n<p style=\"text-align: justify;\">Hence, P (a red face card) = <img decoding=\"async\" style=\"height: 41px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <\/strong>There are only one jack of heart.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcome = 1<\/p>\n<p style=\"text-align: justify;\">Hence, P (the jack of hearts) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(v) <\/strong>There are 13 cards of spade.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcomes = 13<\/p>\n<p style=\"text-align: justify;\">Hence, P (a spade) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(vi) <\/strong>There is only one queen of diamonds.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcome = 1<\/p>\n<p style=\"text-align: justify;\">Hence, P (the queen of diamonds) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image028.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"15_Five_cards_%E2%80%93_then_ten_jack_queen_king_and_ace_of_diamonds_are_well-shuffled_with_their_face_downwards_One_card_is_then_picked_up_at_random\"><\/span><strong>15. Five cards \u2013 then ten, jack, queen, king and ace of diamonds, are well-shuffled with their face downwards. One card is then picked up at random.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) What is the probability that the card is the queen?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace? (b) a queen?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of favourable outcomes = 5<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>There is only one queen.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcome = 1<\/p>\n<p style=\"text-align: justify;\">Hence, P (the queen) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image030.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>In this situation, total number of favourable outcomes = 4<\/p>\n<p style=\"text-align: justify;\">(a) Favourable outcome = 1<\/p>\n<p style=\"text-align: justify;\">Hence, P (an ace) = <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\">(b) There is no card as queen.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcome = 0<\/p>\n<p style=\"text-align: justify;\">Hence, P (the queen) = <img decoding=\"async\" style=\"height: 41px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image032.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"16_12_defective_pens_are_accidently_mixed_with_132_good_ones_It_is_not_possible_to_just_look_at_a_pen_and_tell_whether_or_not_it_is_defective_One_pen_is_taken_out_at_random_from_this_lot_Determine_the_probability_that_the_pen_taken_out_is_a_good_one\"><\/span><strong>16. 12 defective pens are accidently mixed with 132 good ones. It is not possible to just look at a pen and tell whether or not it is defective. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of favourable outcomes = 132 + 12 = 144<\/p>\n<p style=\"text-align: justify;\">Number of favourable outcomes = 132<\/p>\n<p style=\"text-align: justify;\">Hence, P (getting a good pen) = <img decoding=\"async\" style=\"height: 41px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image033.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"17_i_A_lot_of_20_bulbs_contains_4_defective_ones_One_bulb_is_drawn_at_random_from_the_lot_What_is_the_probability_that_this_bulb_is_defective\"><\/span><strong>17. (i) A lot of 20 bulbs contains 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(ii) Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Total number of favourable outcomes = 20<\/p>\n<p style=\"text-align: justify;\">Number of favourable outcomes = 4<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a defective bulb) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image034.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Now total number of favourable outcomes = 20 \u2013 1 = 19<\/p>\n<p style=\"text-align: justify;\">Number of favouroable outcomes = 19 \u2013 4 = 15<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a non-defective bulb) = <img decoding=\"async\" style=\"height: 41px; width: 21px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image035.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"18_A_box_contains_90_discs_which_are_numbered_from_1_to_90_If_one_disc_is_drawn_at_random_from_the_box_find_the_probability_that_it_bears_i_a_two-digit_number_ii_a_perfect_square_number_iii_a_number_divisible_by_5\"><\/span><strong>18. A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears (i) a two-digit number (ii) a perfect square number (iii) a number divisible by 5.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of favourable outcomes = 90<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>Number of two-digit numbers from 1 to 90 are 90 \u2013 9 = 81<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcomes = 81<\/p>\n<p style=\"text-align: justify;\">Hence, P (getting a disc bearing a two-digit number) = <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image036.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>From 1 to 90, the perfect squares are 1, 4, 9, 16, 25, 36, 49, 64 and 81.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcomes = 9<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a perfect square) = <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image037.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong>The numbers divisible by 5 from 1 to 90 are 18.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Favourable outcomes = 18<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a number divisible by 5) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image038.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"19_A_child_has_a_die_whose_six_faces_show_the_letters_as_given_below\"><\/span><strong>19. A child has a die whose six faces show the letters as given below:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>A B C D E A<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>The die is thrown once. What is the probability of getting:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) A? <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) D?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of favourable outcomes = 6<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>Number of favourable outcomes = 2<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a letter A) = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image039.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>Number of favourable outcomes = 1<\/p>\n<p style=\"text-align: justify;\">Hence P (getting a letter D) = <img decoding=\"async\" style=\"height: 41px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image040.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"20_Suppose_you_drop_a_die_at_random_on_the_rectangular_region_shown_in_the_figure_given_on_the_next_page_What_is_the_probability_that_it_will_land_inside_the_circle_with_diameter_1_m\"><\/span><strong>20. Suppose you drop a die at random on the rectangular region shown in the figure given on the next page. What is the probability that it will land inside the circle with diameter 1 m?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 156px; width: 226px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image041.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total area of the given figure (rectangle) = <img decoding=\"async\" style=\"height: 22px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image042.png\" \/><\/p>\n<p style=\"text-align: justify;\">And Area of circle = <img decoding=\"async\" style=\"height: 21px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image043.png\" \/> = <img decoding=\"async\" style=\"height: 49px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image044.png\" \/> = <img decoding=\"async\" style=\"height: 41px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image045.png\" \/> m<sup>2<\/sup><\/p>\n<p style=\"text-align: justify;\">Hence, P (die to land inside the circle) = <img decoding=\"async\" style=\"height: 51px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image046.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"21_A_lot_consists_of_144_ball_pens_of_which_20_are_defective_and_the_others_are_good_Nuri_will_buy_a_pen_if_it_is_good_but_will_not_buy_if_it_is_defective_The_shopkeeper_draws_one_pen_at_random_and_gives_it_to_her_What_is_the_probability_that\"><\/span><strong>21. A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) she will buy it?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) she will not buy it?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of favourable outcomes = 144<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>Number of non-defective pens = 144 \u2013 20 = 124<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Number of favourable outcomes = 124<\/p>\n<p style=\"text-align: justify;\">Hence P (she will buy) = P (a non-defective pen) = <img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>Number of favourable outcomes = 20<\/p>\n<p style=\"text-align: justify;\">Hence P (she will not buy) = P (a defective pen) = <img decoding=\"async\" style=\"height: 41px; width: 64px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image048.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"22_Refer_to_example_13\"><\/span><strong>22. Refer to example 13. <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) Complete the following table:<\/strong><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 2\" style=\"height: 101px; width: 684px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image049.jpg\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) A student argues that \u2018there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore each of them has a probability <img decoding=\"async\" style=\"height: 41px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image050.png\" \/> Do you agree with this argument? Justify your answer.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total favourable outcomes of throwing two dice are:<\/p>\n<p style=\"text-align: justify;\">(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)<\/p>\n<p style=\"text-align: justify;\">(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)<\/p>\n<p style=\"text-align: justify;\">(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)<\/p>\n<p style=\"text-align: justify;\">(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)<\/p>\n<p style=\"text-align: justify;\">(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)<\/p>\n<p style=\"text-align: justify;\">(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>Total number of favourable outcomes = 36<\/p>\n<p style=\"text-align: justify;\"><strong>(i) <\/strong>Favourable outcomes of getting the sum as 3 = 2<\/p>\n<p style=\"text-align: justify;\">Hence P (getting the sum as 3) = <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\">Favourable outcomes of getting the sum as 4 = 3<\/p>\n<p style=\"text-align: justify;\">Hence P (getting the sum as 4) = <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\">Favourable outcomes of getting the sum as 5 = 4<\/p>\n<p style=\"text-align: justify;\">Hence P (getting the sum as 5) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\">Favourable outcomes of getting the sum as 6 = 5<\/p>\n<p style=\"text-align: justify;\">Hence P (getting the sum as 6) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image054.png\" \/><\/p>\n<p style=\"text-align: justify;\">Favourable outcomes of getting the sum as 7 = 6<\/p>\n<p style=\"text-align: justify;\">Hence P (getting the sum as 7) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image055.png\" \/><\/p>\n<p style=\"text-align: justify;\">Favourable outcomes of getting the sum as 9 = 4<\/p>\n<p style=\"text-align: justify;\">Hence P (getting the sum as 9) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image053.png\" \/><\/p>\n<p style=\"text-align: justify;\">Favourable outcomes of getting the sum as 10 = 3<\/p>\n<p style=\"text-align: justify;\">Hence P (getting the sum as 10) = <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\">Favourable outcomes of getting the sum as 11 = 2<\/p>\n<p style=\"text-align: justify;\">Hence P (getting the sum as 11) = <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 3\" style=\"height: 98px; width: 684px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>I do not agree with the argument given here. Justification has already been given in part (i).<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"23_A_game_consists_of_tossing_a_one_rupee_coin_3_times_and_noting_its_outcome_each_time_Hanif_wins_if_all_the_tosses_give_the_same_result_ie_three_heads_or_three_tails_and_loses_otherwise_Calculate_the_probability_that_Hanif_will_lose_the_game\"><\/span><strong>23. A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result, i.e., three heads or three tails and loses otherwise. Calculate the probability that Hanif will lose the game.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>The outcomes associated with the experiment in which a coin is tossed thrice:<\/p>\n<p style=\"text-align: justify;\">HHH, HHT, HTH, THH, TTH, HTT, THT, TTT<\/p>\n<p style=\"text-align: justify;\">Therefore, Total number of favourable outcomes = 8<\/p>\n<p style=\"text-align: justify;\">Number of favourable outcomes = 6<\/p>\n<p style=\"text-align: justify;\">Hence required probability = <img decoding=\"async\" style=\"height: 41px; width: 41px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image021.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"24_A_die_is_thrown_twice_What_is_the_probability_that\"><\/span><strong>24. A die is thrown twice. What is the probability that:&amp;<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) 5 will not come up either time?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) 5 will come up at least once?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> The outcomes associated with the experiment in which a dice is thrown is twice:<\/p>\n<p style=\"text-align: justify;\">(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)<\/p>\n<p style=\"text-align: justify;\">(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)<\/p>\n<p style=\"text-align: justify;\">(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)<\/p>\n<p style=\"text-align: justify;\">(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)<\/p>\n<p style=\"text-align: justify;\">(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)<\/p>\n<p style=\"text-align: justify;\">(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)<\/p>\n<p style=\"text-align: justify;\">Therefore, Total number of favourable outcomes = 36<\/p>\n<p style=\"text-align: justify;\">Now consider the following events:<\/p>\n<p style=\"text-align: justify;\">A = first throe shows 5 and B = second throw shows 5<\/p>\n<p style=\"text-align: justify;\">Therefore, the number of favourable outcomes = 6 in each case.<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/>P(A) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image057.png\" \/>and P(B) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image057.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 16px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image005.png\" \/>P<img decoding=\"async\" style=\"height: 41px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image058.png\" \/>and P<img decoding=\"async\" style=\"height: 41px; width: 53px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image059.png\" \/><\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> Required probability = <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image060.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Let S be the sample space associated with the random experiment of throwing a die twice. Then, n(S) = 36<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image061.png\" \/>B = first and second throw shoe 5, i.e. getting 5 in each throw.<\/p>\n<p style=\"text-align: justify;\">We have, A = (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)<\/p>\n<p style=\"text-align: justify;\">And B = (1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)<\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> P(A) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image057.png\" \/>, P(B) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image057.png\" \/> and P(A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image061.png\" \/>B) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image062.png\" \/><\/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\/10\/mathematics\/ch15\/Ex15.1\/image004.png\" \/> Required probability = Probability that at least one of the two throws shows 5<\/p>\n<p style=\"text-align: justify;\">= P (A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image063.png\" \/>B) = P(A) + P(B) \u2013 P(A<img decoding=\"async\" style=\"height: 13px; width: 17px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image061.png\" \/>B)<\/p>\n<p style=\"text-align: justify;\">= <img decoding=\"async\" style=\"height: 41px; width: 121px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image064.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 10 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"25_Which_of_the_following_arguments_are_correct_and_which_are_not_correct_Give_reasons_for_your_answer\"><\/span><strong>25. Which of the following arguments are correct and which are not correct? Give reasons for your answer:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) If two coins are tossed simultaneously there are three possible outcomes \u2013 two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is <\/strong><img decoding=\"async\" style=\"height: 41px; width: 19px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image065.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) If a die is thrown, there are two possible outcomes \u2013 an odd number or an even number. Therefore, the probability of getting an odd number is <\/strong><img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/10\/mathematics\/ch15\/Ex15.1\/image066.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> <strong>Incorrect<\/strong>: We can classify the outcomes like this but they are not then, \u2018equally likely\u2019. Reason is that \u2018one of each\u2019 can result in two ways \u2013 from a head on first coin and tail on the second coin or from a tail on the first coin and head on the second coin. This makes it twice as likely as two heads (or two tails).<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <strong>Correct<\/strong>: The two outcomes considered in the question are equally likely.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_10_Maths_Exercise_151\"><\/span>NCERT Solutions for Class 10 Maths Exercise 15.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 10 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 10 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 10 Maths have total 15 chapters. 10 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 10 solutions PDF and Maths ncert class 10 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_Class_10\"><\/span>CBSE app for Class 10<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 10 Maths, Computer Science, Home Science,Hindi ,English, Social 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<strong><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\">the best app for CBSE\u00a0<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 10 Maths Exercise 15.1 Class 10 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. 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