{"id":6113,"date":"2023-10-09T04:53:46","date_gmt":"2023-10-09T04:53:46","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=6113"},"modified":"2023-10-09T04:53:46","modified_gmt":"2023-10-09T04:53:46","slug":"ncert-solutions-class-10-maths-chapter-15-probability-ex-15-2","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-15-probability-ex-15-2\/","title":{"rendered":"NCERT Solutions Class 10 Maths Chapter 15 Probability Ex 15.2"},"content":{"rendered":"<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 10 Maths\u00a0<\/span><\/strong><br \/>\n<strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 15 (Probability)\u00a0<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 10 Mathematics <strong>Chapter &#8211; 15 Probability <\/strong>Exercise 15.2 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><strong><span style=\"color: #000000;\">Chapter : 15 Probability<\/span><\/strong><\/p>\n<ul>\n<li><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths-chapter-15-probability-ex-15-1\" target=\"_blank\" rel=\"noopener\">NCERT Class 10 Maths Solution Ex &#8211; 15.1<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><strong><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 15.2<\/span><\/strong><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>1. Two customers, Shyam and Ekta, are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on<br \/>\n<\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>(i) <\/strong>the same day?<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\"><strong>(ii) <\/strong>consecutive days?<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\"><strong>(iii) <\/strong>different days?<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0<\/strong><\/span><span style=\"font-family: Georgia, Palatino;\">Since there are 5 days and both can go to the shop in 5 ways each so,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">The total number of possible outcomes = 5 \u00d7 5 = 25<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>(i)<\/strong> The number of favourable events = 5 (Tue., Tue.), (Wed., Wed.), (Thu., Thu.), (Fri., Fri.), (Sat., Sat.)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">So, P (both visiting on the same day) = 5\/25 = \u2155<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>(ii)<\/strong> The number of favourable events = 8 (Tue., Wed.), (Wed., Thu.), (Thu., Fri.), (Fri., Sat.), (Sat., Fri.), (Fri., Thu.), (Thu., Wed.), and (Wed., Tue.)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">So, P(both visiting on the consecutive days) = 8\/25<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>(iii)<\/strong> P (both visiting on different days) = 1-P (both visiting on the same day)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">So, P (both visiting on different days) = 1-(\u2155) = \u2158<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>2. A die is numbered in such a way that its faces show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times, and the total score in two throws is noted. Complete the following table, which gives a few values of the total score on the two throws:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-6758 \" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/10\/NCERT-Class-10-Maths-Ex15.2-Que-2.png\" alt=\"NCERT Class 10 Maths Solution\" width=\"443\" height=\"230\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/10\/NCERT-Class-10-Maths-Ex15.2-Que-2.png 574w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/10\/NCERT-Class-10-Maths-Ex15.2-Que-2-300x156.png 300w\" sizes=\"auto, (max-width: 443px) 100vw, 443px\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>What is the probability that the total score is<br \/>\n<\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>(i) <\/strong>even?<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\"><strong>(ii) <\/strong>6?<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\"><strong>(iii) <\/strong>at least 6?<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0 <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\">The table will be as follows:<\/span><\/span><\/p>\n<table class=\"table table-bordered\" style=\"width: 30%;\" border=\"1\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">+<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">7<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"color: #000000; font-family: Georgia, Palatino;\">12<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"color: #000000; font-family: Georgia, Palatino; text-align: justify;\">So, the total number of outcomes = 6 \u00d7 6 = 36<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>(i)<\/strong> E (Even) = 18<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">P (Even) = 18\/36 = \u00bd<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>(ii)<\/strong>\u00a0E (sum is 6) = 4<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">P (sum is 6) = 4\/36 = 1\/9<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>(iii)<\/strong>\u00a0E (sum is atleast 6) = 15<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">P (sum is atleast 6) = 15\/36 = 5\/12<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>3. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>is double that of a red ball, determine the number of blue balls in the bag. <\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0 <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\">It is given that the total number of red balls = 5<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Let the total number of blue balls = x<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">So, the total no. of balls = x + 5<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">P(E) = (Number of favourable outcomes\/ Total number of outcomes)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">\u2234 P (drawing a blue ball) = [x\/(x + 5)] \u2014\u2014\u2013(i)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Similarly,<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">P (drawing a red ball) = [5\/(x+5)]\u00a0 \u00a0 \u00a0 \u2014\u2014\u2013(ii)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">From equations (i) and (ii)<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">x = 10<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">So, the total number of blue balls = 10<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>4. A box contains 12 balls, out of which x are black. If one ball is drawn at random from the <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>box, what is the probability that it will be a black ball? <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>If 6 more black balls are put in the box, the probability of drawing a black ball is now <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>double of what it was before. Find x <\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0 <\/strong><\/span>Total Number of balls = 12<\/span><br \/>\n<span style=\"color: #000000;\">Let the number of black balls = x<\/span><br \/>\n<span style=\"color: #000000;\">Probability of getting black ball = Number of possible outcomes \/ Total number of outcomes <\/span><br \/>\n<span style=\"color: #000000;\">= x\/12 <\/span><br \/>\n<span style=\"color: #000000;\">If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before, <\/span><br \/>\n<span style=\"color: #000000;\">Total number of balls = 12 + 6 <\/span><br \/>\n<span style=\"color: #000000;\">Number of black balls = x + 6 <\/span><br \/>\n<span style=\"color: #000000;\">Now, <\/span><br \/>\n<span style=\"color: #000000;\">2 \u00d7 Probability of drawing black ball before = probability of drawing black ball <\/span><br \/>\n<span style=\"color: #000000;\">2 \u00d7 Probability of drawing black ball before = Number of possible outcomes \/Total number of outcomes <\/span><br \/>\n<span style=\"color: #000000;\">2(x\/12) = (x + 6)\/18<\/span><br \/>\n<span style=\"color: #000000;\">3x = x + 6<\/span><br \/>\n<span style=\"color: #000000;\">3x &#8211; x = 6<\/span><br \/>\n<span style=\"color: #000000;\">2x = 6<\/span><br \/>\n<span style=\"color: #000000;\">x = 3 <\/span><br \/>\n<span style=\"color: #000000;\">Hence, previously, the number of black balls was 3. <\/span><br \/>\n<span style=\"color: #000000;\">Thus, the probability of getting a black ball initially was x\/12 = 3\/12 = 1\/4. <\/span><br \/>\n<span style=\"color: #000000;\">Check out more on\u00a0terms of probability.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>5. A jar contains 24 marbles, some are green, and others are blue. If a marble is drawn at <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>random from the jar, the probability that it is green is \u2154. Find the number of blue balls <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\"><strong>in the jar.<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: Georgia, Palatino;\"><strong>Solution &#8211;\u00a0 <\/strong><\/span><span style=\"font-family: Georgia, Palatino;\">Total marbles = 24<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">Let the total green marbles = x<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">So, the total blue marbles = 24 &#8211; x<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">P(getting green marble) = x\/24<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">From the question, x\/24 = \u2154<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">So, the total green marbles = 16<br \/>\n<\/span><span style=\"font-family: Georgia, Palatino;\">And, the total blue marbles = 24 &#8211; 16 = 8<\/span><\/span><\/p>\n<p><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-10-maths\/\" target=\"_blank\" rel=\"noopener\"><b><i>Go Back To Chapters<\/i><\/b><\/a><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 10 Maths\u00a0 Chapter &#8211; 15 (Probability)\u00a0 The NCERT Solutions in English Language for Class 10 Mathematics Chapter &#8211; 15 Probability Exercise 15.2 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter : 15 Probability NCERT Class 10 Maths Solution Ex &#8211; 15.1 Exercise &#8211; 15.2 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1043],"tags":[1045,1120,1122,1044,1049,1048],"class_list":["post-6113","post","type-post","status-publish","format-standard","hentry","category-class-10-maths","tag-class-10-ncert-mathematics-solutions","tag-ncert-class-10-mathematics-chapter-15-probability-solutions","tag-ncert-class-10-mathematics-exercise-15-2-solutions","tag-ncert-class-10-mathematics-solutions-class-10-ncert-solutions","tag-ncert-solutions-class-10-mathematics","tag-ncert-solutions-class-10-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - 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