{"id":4978,"date":"2016-05-19T11:49:00","date_gmt":"2016-05-19T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-15-1\/"},"modified":"2018-06-19T12:46:56","modified_gmt":"2018-06-19T07:16:56","slug":"ncert-solutions-for-class-9-maths-exercise-15-1","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-15-1\/","title":{"rendered":"NCERT Solutions for Class 9 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-9-maths-exercise-15-1\/#NCERT_Solutions_for_Class_9_Mathematics_Probability\" >NCERT Solutions for Class 9 Mathematics Probability<\/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-9-maths-exercise-15-1\/#1_In_a_cricket_match_a_batsman_hits_a_boundary_6_times_out_of_30_balls_he_plays_Find_the_probability_that_he_will\" >1. In a cricket match a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that he will<\/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-9-maths-exercise-15-1\/#2_1500_families_with_2_children_were_selected_randomly_and_the_following_data_were_recorded\" >2. 1500 families with 2 children were selected randomly and the following data were recorded:<\/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-9-maths-exercise-15-1\/#3_In_a_particular_section_of_Class_IX_40_students_were_asked_about_the_months_of_their_birth_and_the_following_graph_was_prepared_for_the_data_so_obtained\" >3. In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:<\/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-9-maths-exercise-15-1\/#4_Three_coins_are_tossed_simultaneously_200_times_with_the_following_frequencies_of_different_outcomes\" >4. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:<\/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-9-maths-exercise-15-1\/#5_An_organization_selected_2400_families_at_random_and_surveyed_them_to_determine_a_relationship_between_income_level_and_the_number_of_vehicles_in_a_family_The_information_gathered_is_listed_in_the_table_below\" >5. An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:<\/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-9-maths-exercise-15-1\/#6_A_teacher_analyses_the_performance_of_two_sections_of_students_in_a_mathematics_test_of_100_marks_given_in_the_following_table\" >6. A teacher analyses the performance of two sections of students in a mathematics test of 100 marks given in the following table:<\/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-9-maths-exercise-15-1\/#7_To_know_the_opinion_of_the_students_about_the_subject_statistics_a_survey_of_200_students_was_conducted_The_data_is_recorded_in_the_following_table\" >7. To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table:<\/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-9-maths-exercise-15-1\/#8_Refer_Q2_Exercise_142_What_is_the_empirical_probability_than_an_engineer_lives\" >8. Refer Q.2, Exercise 14.2. What is the empirical probability than an engineer lives:<\/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-9-maths-exercise-15-1\/#9_Activity_Note_the_frequency_of_two_wheelers_three_wheelers_and_four_wheelers_going_past_during_a_time_interval_in_front_of_your_school_gate_Find_the_probability_that_any_one_vehicle_out_of_the_total_vehicles_you_have_observed_is_a_two_wheeler\" >9. Activity: Note the frequency of two wheelers, three wheelers and four wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two wheeler.<\/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-9-maths-exercise-15-1\/#10_Activity_Ask_all_the_students_in_your_class_room_to_write_a_3-digit_number_Choose_any_student_from_the_room_at_random_What_is_the_probability_that_the_number_written_by_him_is_divisible_by_3_if_the_sum_of_its_digits_is_divisible_by_3\" >10. Activity: Ask all the students in your class room to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by him is divisible by 3, if the sum of its digits is divisible by 3.<\/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-9-maths-exercise-15-1\/#11_Eleven_bags_of_wheat_flour_each_marked_5_kg_actually_contained_the_following_weights_of_four_in_kg_497_505_508_503_500_506_508_498_504_507_500\" >11. Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of four (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00<\/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-9-maths-exercise-15-1\/#12_In_Q5_Exercise_142_you_were_asked_to_prepare_a_frequency_distribution_table_regarding_the_concentration_of_Sulphur_dioxide_in_the_air_in_parts_per_million_of_a_certain_city_for_30_days_Using_this_table_find_the_probability_of_the_concentration_of_Sulphur_dioxide_in_the_interval_012_%E2%80%93_016_on_any_of_these_days\" >12. In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding the concentration of Sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of Sulphur dioxide in the interval 0.12 \u2013 0.16 on any of these days.<\/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-9-maths-exercise-15-1\/#13_In_Q1_Exercise_141_you_were_asked_to_prepare_a_frequency_distribution_table_regarding_the_blood_groups_of_30_students_of_a_class_Use_this_table_to_determine_the_probability_that_a_student_of_this_class_selected_at_random_has_blood_group_AB\" >13. In Q.1, Exercise 14.1 you were asked to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class selected at random has blood group AB.<\/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-15\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-15-1\/#NCERT_Solutions_for_Class_9_Maths_Exercise_151\" >NCERT Solutions for Class 9 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-16\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-for-class-9-maths-exercise-15-1\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 15.1 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 9 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<div style=\"text-align: center;\"><strong>NCERT solutions for Class 9 Maths\u00a0<\/strong><strong>Probability\u00a0<\/strong><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-09-mathematics-probability\/1249\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/div>\n<div><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\" alt=\"NCERT Solutions for Class 9 Maths Exercise 15.1\" width=\"164\" height=\"211\" \/><\/div>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Mathematics_Probability\"><\/span>NCERT Solutions for Class 9 Mathematics Probability<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_In_a_cricket_match_a_batsman_hits_a_boundary_6_times_out_of_30_balls_he_plays_Find_the_probability_that_he_will\"><\/span><strong>1. In a cricket match a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that he will <\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) hit a boundary in the next ball.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) not hit boundary in the next ball.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>For all solutions, Probability = <img decoding=\"async\" style=\"height: 41px; width: 144px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image001.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> Number of times on boundary is hit = 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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (hit a boundary) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> Number of times on boundary is not hit = 30 \u2013 6 = 24<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (did not hit a boundary) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image004.png\" \/><\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_1500_families_with_2_children_were_selected_randomly_and_the_following_data_were_recorded\"><\/span><strong>2. 1500 families with 2 children were selected randomly and the following data were recorded:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 1\" style=\"height: 100px; width: 309px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image005.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Compute the probability of a family, chosen at random, having:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) 2 girls (ii) 1 girl (iii) No girl<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Also check whether the sum of these probabilities is 1.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> Total number of families = 1500<\/p>\n<p style=\"text-align: justify;\">No. of families having 2 girls = 475<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (Family having 2 girls) = <img decoding=\"async\" style=\"height: 41px; width: 72px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> No of families having 1 girl = 814<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (Family having 1 girl) = <img decoding=\"async\" style=\"height: 41px; width: 80px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> No. of families having no girl = 211<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (Family having no girl) = <img decoding=\"async\" style=\"height: 41px; width: 37px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image008.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Checking<\/strong>: Sum of all probabilities = <img decoding=\"async\" style=\"height: 41px; width: 111px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>= <img decoding=\"async\" style=\"height: 41px; width: 155px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image010.png\" \/> <\/strong>= 1<\/p>\n<p style=\"text-align: justify;\">Yes, the sum of probabilities is 1.<\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_In_a_particular_section_of_Class_IX_40_students_were_asked_about_the_months_of_their_birth_and_the_following_graph_was_prepared_for_the_data_so_obtained\"><\/span><strong>3. In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong><img decoding=\"async\" id=\"Picture 4\" style=\"height: 227px; width: 381px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image011.jpg\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Find the probability that a student of the class was born in August.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>From the bar graph, we observe,<\/p>\n<p style=\"text-align: justify;\">Total no. of students of Class IX = 40<\/p>\n<p style=\"text-align: justify;\">No. of students of Class IX born in August = 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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (A student born in August) = <img decoding=\"async\" style=\"height: 41px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image012.png\" \/><\/p>\n<hr \/>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Three_coins_are_tossed_simultaneously_200_times_with_the_following_frequencies_of_different_outcomes\"><\/span><strong>4. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 2\" style=\"height: 105px; width: 191px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image013.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>No. of 2 heads = 72<\/p>\n<p style=\"text-align: justify;\">Total number of outcomes = 23 + 72 + 77 + 28 = 200<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (2 heads) = <img decoding=\"async\" style=\"height: 41px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image014.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_An_organization_selected_2400_families_at_random_and_surveyed_them_to_determine_a_relationship_between_income_level_and_the_number_of_vehicles_in_a_family_The_information_gathered_is_listed_in_the_table_below\"><\/span><strong>5. An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 5\" style=\"height: 161px; width: 397px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image015.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Suppose a family is chosen. Find the probability that the family chosen is:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) earning Rs. 10000 \u2013 13000 per month and owning exactly 2 vehicles.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) earning Rs. 16000 or more per month and owning exactly 1 vehicle.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) earning less than Rs. 7000 per month and does not own any vehicle.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) earning Rs. 13000 \u2013 16000 per month and owning more than 2 vehicles.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) not more than 1 vehicle.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> P (earning Rs. 10000 \u2013 13000 per month and owning exactly 2 vehicles) = <img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image016.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> P (earning Rs. 16000 or more per month and owning exactly 1 vehicles) = <img decoding=\"async\" style=\"height: 41px; width: 40px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> P (earning Rs. 7000 per month and does not own any vehicles) = <img decoding=\"async\" style=\"height: 41px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image018.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> P (earning Rs. 13000 \u2013 16000 per month and owning more than 2 vehicles) = <img decoding=\"async\" style=\"height: 41px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(v)<\/strong> P (owning not more than 1 vehicle) = <img decoding=\"async\" style=\"height: 41px; width: 88px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image020.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"6_A_teacher_analyses_the_performance_of_two_sections_of_students_in_a_mathematics_test_of_100_marks_given_in_the_following_table\"><\/span><strong>6. A teacher analyses the performance of two sections of students in a mathematics test of 100 marks given in the following table:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 6\" style=\"height: 206px; width: 247px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image021.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(i) Find the probability that a student obtained less than 20% in the mathematics test.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) Find the probability that a student obtained 60 or above.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> No. of students obtaining marks less than 20 out of 100, i.e. 20% = 7<\/p>\n<p style=\"text-align: justify;\">Total students in the class = 90<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (A student obtained less than 20%) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> No. of students obtaining marks 60 or above = 15 + 8 = 23<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (A student obtained marks 60 or above) = <img decoding=\"async\" style=\"height: 41px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image023.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"7_To_know_the_opinion_of_the_students_about_the_subject_statistics_a_survey_of_200_students_was_conducted_The_data_is_recorded_in_the_following_table\"><\/span><strong>7. To know the opinion of the students about the subject statistics, a survey of 200 students was conducted. The data is recorded in the following table:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 7\" style=\"height: 78px; width: 218px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image024.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>Find the probability that a student chosen at random:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) likes statistics (ii) dislikes it.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total no. of students on which the survey about the subject of statistics was conducted = 200<\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> No. of students who like statistics = 135<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (a student likes statistics) = <img decoding=\"async\" style=\"height: 41px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image025.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> No. of students who do not like statistics = 65<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (a student does not like statistics) = <img decoding=\"async\" style=\"height: 41px; width: 65px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image026.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"8_Refer_Q2_Exercise_142_What_is_the_empirical_probability_than_an_engineer_lives\"><\/span><strong>8. Refer Q.2, Exercise 14.2. What is the empirical probability than an engineer lives:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) less than 7 km from her place of work?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) more than or equal to 7 km from her place of work?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) within <\/strong><img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image027.png\" \/><strong> km from her place of work?<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Total number of engineers = 40<\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> No. of engineers living less than 7 km from her place of work = 9<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (Engineer living less than 7 km from her place of work) = <img decoding=\"async\" style=\"height: 41px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image028.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> No. of engineers living more than or equal to 7 km from her place of work = 21<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (Engineer living more than or equal to 7 km from her place of work) = <img decoding=\"async\" style=\"height: 41px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> No. of engineers living within <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image027.png\" \/> km from her place of work = 0<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 13px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (Engineer living within <img decoding=\"async\" style=\"height: 41px; width: 16px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image027.png\" \/> km from her place of work) = <img decoding=\"async\" style=\"height: 41px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image030.png\" \/> = 0<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"9_Activity_Note_the_frequency_of_two_wheelers_three_wheelers_and_four_wheelers_going_past_during_a_time_interval_in_front_of_your_school_gate_Find_the_probability_that_any_one_vehicle_out_of_the_total_vehicles_you_have_observed_is_a_two_wheeler\"><\/span><strong>9. Activity: Note the frequency of two wheelers, three wheelers and four wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two wheeler.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let you noted the frequency of types of wheelers after school time (i.e. 3 pm to 3.30 pm) for half an hour.<\/p>\n<p style=\"text-align: justify;\">Let the following table shows the frequency of wheelers.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" id=\"Picture 8\" style=\"height: 88px; width: 312px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image031.png\" \/><\/p>\n<p style=\"text-align: justify;\">Probability that a two wheelers passes after this interval = <img decoding=\"async\" style=\"height: 41px; width: 57px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image032.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"10_Activity_Ask_all_the_students_in_your_class_room_to_write_a_3-digit_number_Choose_any_student_from_the_room_at_random_What_is_the_probability_that_the_number_written_by_him_is_divisible_by_3_if_the_sum_of_its_digits_is_divisible_by_3\"><\/span><strong>10. Activity: Ask all the students in your class room to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by him is divisible by 3, if the sum of its digits is divisible by 3.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Let number of students in your class is 24.<\/p>\n<p style=\"text-align: justify;\">Let 3-digit number written by each of them is as follows:<\/p>\n<p style=\"text-align: justify;\">837, 172, 643, 371, 124, 512, 432, 948, 311, 252, 999, 557, 784, 928, 867, 798, 665, 245, 107, 463, 267, 523, 944, 314<\/p>\n<p style=\"text-align: justify;\">Numbers divisible by 3 are = 837, 432, 948, 252, 999, 867, 798 and 267<\/p>\n<p style=\"text-align: justify;\">Number of 3-digit numbers divisible by 3 = 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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (3-digit numbers divisible by 3) = <img decoding=\"async\" style=\"height: 41px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image033.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"11_Eleven_bags_of_wheat_flour_each_marked_5_kg_actually_contained_the_following_weights_of_four_in_kg_497_505_508_503_500_506_508_498_504_507_500\"><\/span><strong>11. Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of four (in kg): 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Find the probability that any of these bags chosen at random contains more than 5 kg of flour.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Number of bags containing more than 5 kg of wheat flour = 7<\/p>\n<p style=\"text-align: justify;\">Total number of wheat flour bags = 11<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (a bag containing more than 5 kg of wheat flour) = <img decoding=\"async\" style=\"height: 41px; width: 20px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image034.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"12_In_Q5_Exercise_142_you_were_asked_to_prepare_a_frequency_distribution_table_regarding_the_concentration_of_Sulphur_dioxide_in_the_air_in_parts_per_million_of_a_certain_city_for_30_days_Using_this_table_find_the_probability_of_the_concentration_of_Sulphur_dioxide_in_the_interval_012_%E2%80%93_016_on_any_of_these_days\"><\/span><strong>12. In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding the concentration of Sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of Sulphur dioxide in the interval 0.12 \u2013 0.16 on any of these days.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>From the frequency distribution table we observe that:<\/p>\n<p style=\"text-align: justify;\">No. of days during which the concentration of Sulphur dioxide lies in interval 0.12 \u2013 0.16 = 2<\/p>\n<p style=\"text-align: justify;\">Total no. of days during which concentration of Sulphur dioxide recorded = 30<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (day when concentration of Sulphur dioxide (in ppm) lies in 0.12 \u2013 0.16) = <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image035.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 15.1<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"13_In_Q1_Exercise_141_you_were_asked_to_prepare_a_frequency_distribution_table_regarding_the_blood_groups_of_30_students_of_a_class_Use_this_table_to_determine_the_probability_that_a_student_of_this_class_selected_at_random_has_blood_group_AB\"><\/span><strong>13. In Q.1, Exercise 14.1 you were asked to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class selected at random has blood group AB.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>From the frequency distribution table we observe that:<\/p>\n<p style=\"text-align: justify;\">Number of students having blood group AB = 3<\/p>\n<p style=\"text-align: justify;\">Total number of students whose blood group were recorded = 30<\/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\/09\/maths\/ch15\/Ex15.1\/image002.png\" \/> P (a student having blood group AB) = <img decoding=\"async\" style=\"height: 41px; width: 56px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch15\/Ex15.1\/image036.png\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_151\"><\/span>NCERT Solutions for Class 9 Maths Exercise 15.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions for Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 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_9\"><\/span>CBSE app for Class 9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 9 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<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 for Class 9 Maths Exercise 15.1 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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