{"id":2067,"date":"2021-12-23T16:28:16","date_gmt":"2021-12-23T10:58:16","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2067"},"modified":"2023-12-26T14:06:28","modified_gmt":"2023-12-26T08:36:28","slug":"ncert-solutions-for-class-12-maths-chapter-13-probability-13-1","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-1\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.1"},"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-13-1\/#NCERT_Solutions_for_Class_12_Maths_Chapter_Probability_Exercise_131\" title=\"NCERT Solutions for Class 12 Maths Chapter Probability Exercise 13.1\">NCERT Solutions for Class 12 Maths Chapter Probability Exercise 13.1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><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-13-1\/#FAQs_on_NCERT_Solutions_Class_12_Maths_Chapter_13_Probability_Exercise_131\" title=\"FAQs on NCERT Solutions Class 12 Maths Chapter 13 Probability Exercise 13.1\">FAQs on NCERT Solutions Class 12 Maths Chapter 13 Probability Exercise 13.1<\/a><ul class='ez-toc-list-level-3'><li class='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-13-1\/#What_are_the_various_properties_of_Conditional_Probability\" title=\"What are the various properties of Conditional Probability?\">What are the various properties of Conditional Probability?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-1\/#What_concepts_can_I_Learn_using_these_NCERT_Solutions\" title=\"What concepts can I Learn using these NCERT Solutions?\">What concepts can I Learn using these NCERT Solutions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-1\/#What_is_the_multiplication_theorem\" title=\"What is the multiplication theorem?\">What is the multiplication theorem?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>You can find answers to all the exercise questions in Chapter 13.1 on Probability in the <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\"><strong>NCERT Solutions for Class 12 Maths<\/strong><\/a>. The concepts covered in Chapter 13 serve as the basis for solving the exercises in Chapter 13.1 of NCERT Solutions for Class 12. This practice is essential for preparing for both the CBSE Term II exam and various competitive exams. To improve your exam performance, you can download these NCERT Solutions and practice them offline.<\/p>\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\/2067\" 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-13.1.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-13.1.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 13.1<br\/><\/a>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_Probability_Exercise_131\"><\/span>NCERT Solutions for Class 12 Maths Chapter Probability Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Utilizing <strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/\">NCERT Solutions for Class 12<\/a><\/strong> Mathematics, specifically Exercise 13.1, proves to be the optimal choice for CBSE students gearing up for their examinations. This particular chapter encompasses a variety of exercises, and among them lies Exercise 13.1, the solutions of which are readily accessible in PDF format on this webpage. Additionally, these solutions can be conveniently downloaded from our website or app.<\/p>\n<p><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>NCERT solutions<\/strong><\/a> for Exercise 13.1 have been meticulously crafted by subject matter experts at Infinity Learn, meticulously aligning with CBSE guidelines. Students who diligently prepare by working through all the exercises in this chapter are well-positioned to secure favorable exam results. These solutions offer valuable insights into the question patterns and the chapter&#8217;s weightage in terms of marks, aiding students in their preparation.<\/p>\n<p>In addition to Exercise 13.1, this chapter presents a plethora of exercises brimming with numerous questions, all of which have been expertly curated, as mentioned earlier. Consequently, these solutions are recognized for their exceptional quality, and it is imperative that students make use of them. To excel in the exam, thorough practice of these solutions and diligent tackling of all accompanying questions is essential. Delay no further; obtain the NCERT solutions for Class 12 Mathematics Chapter 13, Exercise 13.1, from the Infinity Learn website to enhance your exam readiness. If you have the app on your phone, ensure to download it through the app as well. These solutions can be employed both online and offline, providing flexibility in your preparation process.<\/p>\n<ul>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-2\/\"><strong>Exercise 13.2 solutions<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-3\/\"><strong>Exercise 13.3 solutions<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-4\/\"><strong>Exercise 13.4 solutions<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-5\/\"><strong>Exercise 13.5 solutions<\/strong><\/a><\/li>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-miscellaneous\"><strong>Miscellaneous Exercise solutions<\/strong><\/a><\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_NCERT_Solutions_Class_12_Maths_Chapter_13_Probability_Exercise_131\"><\/span>FAQs on NCERT Solutions Class 12 Maths Chapter 13 Probability Exercise 13.1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_are_the_various_properties_of_Conditional_Probability\"><\/span>What are the various properties of Conditional Probability?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe different properties of Conditional Probability are:\u202f Let A and B be events of a sample space S of an experiment, then;  Property 1: P(S|B) = P(B|B) = 1  Property 2: If E and F are two events in a sample space S and B is an event of S, such that P(B)\u22600, then;  P((E \u222a F)|B) = P(E|B) + P(F|B) \u2013 P((E \u2229 F)|B)  Property 3: P(A\u2032|B) = 1 \u2212 P(A|B) \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_concepts_can_I_Learn_using_these_NCERT_Solutions\"><\/span>What concepts can I Learn using these NCERT Solutions?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe following concepts are dealing in NCERT Solutions for Class 12 Maths Chapter 13 for the students:\u202f  Conditional probability and its properties\u202f  Multiplication theorem,\u202f  Independent events,  Bayes\u2019 Theorem,  Partition of a space,  Random variables, their probability, distributions, and their mean\/variance\u202f,  Bernoulli trials,  Binomial distribution, \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_multiplication_theorem\"><\/span>What is the multiplication theorem?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe multiplication theorem of probability help us to explain the condition relating to two events. Considering two events, i.e., A and B belonging to the sample space denoted by S, set A\u2229B are the events where both event A, as well as event B, take place. Therefore, (A\u2229B) belongs to the occurrence of event A and event B simultaneously. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the various properties of Conditional Probability?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The different properties of Conditional Probability are:\u202f Let A and B be events of a sample space S of an experiment, then;  Property 1: P(S|B) = P(B|B) = 1  Property 2: If E and F are two events in a sample space S and B is an event of S, such that P(B)\u22600, then;  P((E \u222a F)|B) = P(E|B) + P(F|B) \u2013 P((E \u2229 F)|B)  Property 3: P(A\u2032|B) = 1 \u2212 P(A|B)\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What concepts can I Learn using these NCERT Solutions?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The following concepts are dealing in NCERT Solutions for Class 12 Maths Chapter 13 for the students:\u202f  Conditional probability and its properties\u202f  Multiplication theorem,\u202f  Independent events,  Bayes\u2019 Theorem,  Partition of a space,  Random variables, their probability, distributions, and their mean\/variance\u202f,  Bernoulli trials,  Binomial distribution,\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the multiplication theorem?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The multiplication theorem of probability help us to explain the condition relating to two events. Considering two events, i.e., A and B belonging to the sample space denoted by S, set A\u2229B are the events where both event A, as well as event B, take place. Therefore, (A\u2229B) belongs to the occurrence of event A and event B simultaneously.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>You can find answers to all the exercise questions in Chapter 13.1 on Probability in the NCERT Solutions for Class [&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":"exercise 13.1 class 12 maths","_yoast_wpseo_title":"NCERT Solutions Class 12 Maths Chapter 13 Probability Exercise 13.1","_yoast_wpseo_metadesc":"NCERT Solutions for Class 12 Maths, Chapter 13 (Probability), Exercise 13.1, offers detailed answers and explanations.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-1\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the 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