{"id":2069,"date":"2021-12-23T16:28:57","date_gmt":"2021-12-23T10:58:57","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2069"},"modified":"2024-07-03T12:33:15","modified_gmt":"2024-07-03T07:03:15","slug":"ncert-solutions-for-class-12-maths-chapter-13-probability-13-2","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-2\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.2"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\">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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><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><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-2\/#NCERT_Solutions_for_Class_12_Maths_Chapter_13_Exercise_132_-_Free_PDF_Download\" title=\"NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.2 \u2013 Free PDF Download\">NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.2 \u2013 Free PDF Download<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-2\/#Access_NCERT_Solutions_for_Class_12_Maths_Chapter_Probability_132\" title=\"Access NCERT Solutions for Class 12 Maths Chapter Probability 13.2\">Access NCERT Solutions for Class 12 Maths Chapter Probability 13.2<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-2\/#NCERT_Solutions_Class_12_Maths_Chapter_13_Exercise_132_Tips\" title=\"NCERT Solutions Class 12 Maths Chapter 13 Exercise 13.2 Tips\">NCERT Solutions Class 12 Maths Chapter 13 Exercise 13.2 Tips<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>Exercise 13.2 of <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\"><strong>NCERT Solutions for Class 12 Maths<\/strong><\/a> Chapter 13 \u2013 Probability covers the following topics:<\/p>\n<ol>\n<li><strong>Multiplication Theorem on Probability<\/strong><\/li>\n<li><strong>Independent Events:<\/strong> These are events where the probability of one occurring is not influenced by the occurrence of the other.<\/li>\n<\/ol>\n<p>This exercise contains problems focused on these topics, helping students understand and apply probability concepts in real-life scenarios.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_13_Exercise_132_-_Free_PDF_Download\"><\/span>NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.2 \u2013 Free PDF Download<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? 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wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/2069\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Exercise-13.2.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Exercise-13.2.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Exercise 13.2<br\/><\/a>\n<h3><span class=\"ez-toc-section\" id=\"Access_NCERT_Solutions_for_Class_12_Maths_Chapter_Probability_132\"><\/span>Access NCERT Solutions for Class 12 Maths Chapter Probability 13.2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. If P (A) = 3\/5 and P (B) = 1\/5, find P (A \u2229 B) if A and B are independent events.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given P (A) = 3\/5 and P (B) = 1\/5<\/p>\n<p>As A and B are independent events.<\/p>\n<p>\u21d2 P (A \u2229 B) = P (A).P (B)<\/p>\n<p>= 3\/5 \u00d7 1\/5 = 3\/25<\/p>\n<p><strong>2. A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given a box of oranges.<\/p>\n<p>Let A, B and C denotes the events respectively that the first, second and third drawn orange is good.<\/p>\n<p>Now, P (A) = P (good orange in first draw) = 12\/15<\/p>\n<p>Because the second orange is drawn without replacement, now the total number of good oranges will be 11, and the total oranges will be 14; that is the conditional probability of B, given that A has already occurred.<\/p>\n<p>Now, P (B\/A) = P (good orange in second draw) = 11\/14<\/p>\n<p>Because the third orange is drawn without replacement, now the total number of good oranges will be 10, and the total oranges will be 13; that is the conditional probability of C, given that A and B have already occurred.<\/p>\n<p>Now, P (C\/AB) = P (good orange in third draw) = 10\/13<\/p>\n<p>Thus the probability that all the oranges are good.<\/p>\n<p>\u21d2 P (A \u2229 B \u2229 C) = 12\/15 \u00d7 11\/14 \u00d7 10\/13 = 44\/91<\/p>\n<p>Hence, the probability that a box will be approved for sale = 44\/91<\/p>\n<p><strong>3. A fair coin and an unbiased die are tossed. Let A be the event \u2018head appears on the coin\u2019 and B be the event \u20183 on the die\u2019. Check whether A and B are independent events or not.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Given a fair coin and an unbiased die are tossed.<\/p>\n<p>We know that the sample space S:<\/p>\n<p>S = {(H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}<\/p>\n<p>Let A be the event head that appears on the coin:<\/p>\n<p>\u21d2 A = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6)}<\/p>\n<p>\u21d2 P (A) = 6\/12 = \u00bd<\/p>\n<p>Now, Let B be the event 3 on the die<\/p>\n<p>\u21d2 B = {(H, 3), (T, 3)}<\/p>\n<p>\u21d2 P (B) = 2\/12 = 1\/6<\/p>\n<p>As, A \u2229 B = {(H, 3)}<\/p>\n<p>\u21d2 P (A \u2229 B) = 1\/12 \u2026\u2026 (1)<\/p>\n<p>And P (A). P (B) = \u00bd \u00d7 1\/6 = 1\/12 \u2026\u2026 (2)<\/p>\n<p>From (1) and (2) P (A \u2229 B) = P (A). P (B)<\/p>\n<p>Therefore, A and B are independent events.<\/p>\n<p><strong>4. A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, \u2018the number is even,\u2019 and B be the event, \u2018the number is red\u2019. Are A and B independent?<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>The sample space for the dice will be<\/p>\n<p>S = {1, 2, 3, 4, 5, 6}<\/p>\n<p>Let A be the event, the number is even:<\/p>\n<p>\u21d2 A = {2, 4, 6}<\/p>\n<p>\u21d2 P (A) = 3\/6 = \u00bd<\/p>\n<p>Now, Let B be the event the number is red:<\/p>\n<p>\u21d2 B = {1, 2, 3}<\/p>\n<p>\u21d2 P (B) = 3\/6 = 1\/2<\/p>\n<p>As, A \u2229 B = {2}<\/p>\n<p>\u21d2 P (A \u2229 B) = 1\/6 \u2026\u2026.. (1)<\/p>\n<p>And P (A). P (B) = \u00bd \u00d7 \u00bd = \u00bc \u2026.. (2)<\/p>\n<p>From (1) and (2) P (A \u2229 B) \u2260 P (A). P (B)<\/p>\n<p>Therefore, A and B are not independent events.<\/p>\n<p><strong>5. The probability of obtaining an even prime number on each die, when a pair of dice is rolled is<br \/>\nA. 0<br \/>\nB. 1\/3<br \/>\nC. 1\/12<br \/>\nD. 1\/36<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>D. 1\/36<\/p>\n<p><strong>Explanation:<\/strong><\/p>\n<p>Given A pair of dice is rolled.<\/p>\n<p>Hence the number of outcomes = 36<\/p>\n<p>Let P (E) be the probability of getting an even prime number on each die.<\/p>\n<p>As we know, the only even prime number is 2.<\/p>\n<p>So, E = {2, 2}<\/p>\n<p>\u21d2 P \u20ac = 1\/36<\/p>\n<h3><span class=\"ez-toc-section\" id=\"NCERT_Solutions_Class_12_Maths_Chapter_13_Exercise_132_Tips\"><\/span>NCERT Solutions Class 12 Maths Chapter 13 Exercise 13.2 Tips<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability\/\"><strong>NCERT Solutions for Class 12 Maths Chapter 13<\/strong><\/a> Exercise 13.2 is an excellent resource prepared by experts to help students understand independent events and the multiplication theorem. These reliable guides enable students to solve problems independently and are essential for scoring well in exams.<\/p>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>NCERT solutions<\/strong><\/a> aid in learning the properties, terms, and definitions related to independent events and their applications. The exemplar problems in Chapter 13 require a good understanding of conditional probability, making it crucial to grasp the concepts from the previous exercise thoroughly. Download the Infinity Learn NCERT Solutions PDF for free and start learning today.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Exercise 13.2 of NCERT Solutions for Class 12 Maths Chapter 13 \u2013 Probability covers the following topics: Multiplication Theorem on [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"NCERT Solutions for Class 12 Maths","_yoast_wpseo_title":"NCERT Solutions for Class 12 Maths Ch-13 Probability Exercise 13.2","_yoast_wpseo_metadesc":"NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.2 covers the multiplication theorem on probability and independent events, offering real-life application problems for better 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