{"id":2073,"date":"2021-12-23T16:29:42","date_gmt":"2021-12-23T10:59:42","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2073"},"modified":"2023-12-26T14:06:25","modified_gmt":"2023-12-26T08:36:25","slug":"ncert-solutions-for-class-12-maths-chapter-13-probability-13-3","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-3\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 13 Probability Exercise 13.3"},"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-13-3\/#NCERT_Solutions_for_Class_12_Maths_Chapter_Probability_133\" title=\"NCERT Solutions for Class 12 Maths Chapter Probability 13.3\">NCERT Solutions for Class 12 Maths Chapter Probability 13.3<\/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-13-3\/#FAQs_on_NCERT_Solutions_for_Class_12_Maths_Chapter_13_Exercise_133\" title=\"FAQs on NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.3\">FAQs on NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.3<\/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-13-3\/#What_are_the_topics_covered_in_class_12_maths_chapter_13\" title=\"What are the topics covered in class 12 maths chapter 13?\">What are the topics covered in class 12 maths chapter 13?<\/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-13-3\/#What_are_the_benefits_of_solving_NCERT_solutions_by_Infinity_Learn\" title=\"What are the benefits of solving NCERT solutions by Infinity Learn?\">What are the benefits of solving NCERT solutions by Infinity Learn?<\/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-13-3\/#How_can_I_download_the_NCERT_Solutions_of_this_exercise_from_the_Infinity_Learn_website\" title=\" How can I download the NCERT Solutions of this exercise from the Infinity Learn website?\"> How can I download the NCERT Solutions of this exercise from the Infinity Learn website?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>You can find answers to all the exercise questions in NCERT Solutions for Class 12 Maths Chapter 13, specifically in section 13.3 on Probability. The concepts introduced in Chapter 13 serve as the basis for solving problems in <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/\"><strong>NCERT Solutions for Class 12<\/strong><\/a> in the 13.3 Exercise section. This practice is essential not only for success in the CBSE Term II exam but also for competitive exams. To prepare effectively for your exams, you should download these NCERT Solutions and use them for offline practice.<\/p>\n\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? Are you preparing for Exams?<\/span>\n\t\t\t<span class=\"subtitle\">Study without Internet (Offline)<\/span>\n\t\t\t\n\t\t\t<button class=\"download-pdf-btn\" type=\"submit\"><img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/themes\/blog\/assets\/download-icon.svg\" alt=\"Download PDF icon\" width=\"18px\" height=\"18px\">Download PDF<\/button>\n\t\t<\/div>\n\t\t<div class=\"custom-model-main pdf-download-modal\">\n\t\t\t<div class=\"custom-model-inner\">\n\t\t\t\t<div class=\"close-modal-btn close-pdf-btn\">\u00d7<\/div>\n\t\t\t\t<div class=\"custom-model-wrap\">\n\t\t\t\t\t<div class=\"pop-up-content-wrap\">\n\t\t\t\t\t<div role=\"form\" class=\"wpcf7\" id=\"wpcf7-f314520-o1\" lang=\"en-US\" dir=\"ltr\">\n<div class=\"screen-reader-response\"><p role=\"status\" aria-live=\"polite\" aria-atomic=\"true\"><\/p> <ul><\/ul><\/div>\n<form action=\"\/surge\/wp-json\/wp\/v2\/posts\/2073#wpcf7-f314520-o1\" method=\"post\" class=\"wpcf7-form init\" novalidate=\"novalidate\" 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class=\"otp_message\"><\/div>\n<p><label>Preferred time slot for the call<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap timeslot\"><select name=\"timeslot\" class=\"wpcf7-form-control wpcf7-select\" aria-invalid=\"false\"><option value=\"\">---<\/option><option value=\"9 am\">9 am<\/option><option value=\"10 am\">10 am<\/option><option value=\"11 am\">11 am<\/option><option value=\"12 pm\">12 pm<\/option><option value=\"1 pm\">1 pm<\/option><option value=\"2 pm\">2 pm<\/option><option value=\"3 pm\">3 pm<\/option><option value=\"4 pm\">4 pm<\/option><option value=\"5 pm\">5 pm<\/option><option value=\"6 pm\">6 pm<\/option><option value=\"7 pm\">7 pm<\/option><option value=\"8pm\">8pm<\/option><option value=\"9 pm\">9 pm<\/option><option value=\"10pm\">10pm<\/option><\/select><\/span><\/p>\n<p><label>Please indicate your interest<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap intent-checkbox\"><span class=\"wpcf7-form-control wpcf7-checkbox\"><span 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value=\"Hindi\">Hindi<\/option><option value=\"Marathi\">Marathi<\/option><option value=\"Tamil\">Tamil<\/option><option value=\"Telugu\">Telugu<\/option><option value=\"Malayalam\">Malayalam<\/option><\/select><\/span><\/p>\n<p><label>Are you a Sri Chaitanya student?<\/label><br \/>\n<span class=\"wpcf7-form-control-wrap sri-chaitanya-student\"><select name=\"sri-chaitanya-student\" class=\"wpcf7-form-control wpcf7-select\" aria-invalid=\"false\"><option value=\"No\">No<\/option><option value=\"Yes\">Yes<\/option><\/select><\/span><\/p>\n<style>\n.intent-checkbox .wpcf7-checkbox{\n    display: flex;\n    flex-wrap: wrap;\n}\n.intent-checkbox .wpcf7-checkbox .wpcf7-list-item {\n    width: 50%;\n    margin: 0!important;\n    padding: 0.1rem;\n}\n<\/style>\n<p class=\"verify_otp_input\">Verify OTP Code (required)<br \/><span class=\"wpcf7-form-control-wrap phone_verify\"><input type=\"number\" name=\"phone_verify\" value=\"\" class=\"wpcf7-form-control wpcf7-number 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\/2073\" 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-13.3.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-13.3.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 13.3<br\/><\/a>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_12_Maths_Chapter_Probability_133\"><\/span>NCERT Solutions for Class 12 Maths Chapter Probability 13.3<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Utilizing <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/\"><strong>NCERT solutions for Class 12 Mathematics<\/strong><\/a> Exercise 13.3 proves to be the most advantageous choice for CBSE students who are gearing up for their exams. This chapter encompasses multiple exercises, with Exercise 13.3 being one of them. You can readily access its solutions in PDF format on this webpage, or alternatively, you have the option to download these solutions from our website or app. The dedicated experts at Infinity Learn have meticulously crafted these solutions, ensuring strict adherence to CBSE guidelines.<\/p>\n<p>Students in Class 12 who diligently complete all the exercises provided in this chapter position themselves to excel in their examinations. These solutions offer invaluable insights into the question patterns and weightage of marks allocated to this chapter&#8217;s content, thereby facilitating thorough preparation.<\/p>\n<p>In addition to Exercise 13.3, this chapter contains a multitude of exercises, each featuring numerous questions. It is important to note that all these solutions have been meticulously curated by subject matter experts, reinforcing their superior quality. It is highly recommended that students extensively practice these solutions to secure a commendable performance in their exams. Furthermore, it is imperative to tackle all accompanying questions adjacent to the exercises.<\/p>\n<p>There is no need for delay; seize the opportunity to download the <a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\"><strong>NCERT solutions<\/strong><\/a> for Class 12 Mathematics Chapter 13 Exercise 13.3 from the Infinity Learn website promptly to enhance your exam readiness. If you happen to possess the Infinity Learn app on your mobile device, make sure to acquire the solutions through the app as well. These solutions are versatile, allowing for both online and offline utilization.<\/p>\n<p><strong>Also Check:<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-1\/\"><strong>Exercise 13.1 solutions<\/strong><\/a><\/li>\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-13-4\/\"><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_for_Class_12_Maths_Chapter_13_Exercise_133\"><\/span>FAQs on NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.3<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_topics_covered_in_class_12_maths_chapter_13\"><\/span>What are the topics covered in class 12 maths chapter 13?<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\the chapter begins with the introduction of probability where you came to know about the discovery of probability. Later, you got to know what conditional probability is and what are its properties. After that, the multiplication theorem on probability begins the discussion of independent events. You will Learn about the Bayes theorem which is categorized into smaller sections like the partition of sample space and theorem of total probability. The chapter gets over with probability distribution of random variables, mean of random variables, the variance of random variables, Bernoulli's Trials, and 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_are_the_benefits_of_solving_NCERT_solutions_by_Infinity_Learn\"><\/span>What are the benefits of solving NCERT solutions by Infinity Learn?<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\tNCERT solutions by Infinity Learn are designed strictly according to the latest CBSE syllabus and it is the best way to study this chapter containing all the important points and formulas. The subject matter experts designed these NCERT solutions with the aim to make the learning process the most convenient way.  \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=\"How_can_I_download_the_NCERT_Solutions_of_this_exercise_from_the_Infinity_Learn_website\"><\/span> How can I download the NCERT Solutions of this exercise from the Infinity Learn website?<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\tIt is very easy to download the NCERT Solutions of this exercise from the Infinity Learn website. You just have to come at Infinity Learn official website and look for the Class 12 category under the \u2018NCERT Solutions\u2019 section. After that, you can easily use these Solutions. Downloading these solutions and studying at your convenience is our main aim.\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 topics covered in class 12 maths chapter 13?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"he chapter begins with the introduction of probability where you came to know about the discovery of probability. Later, you got to know what conditional probability is and what are its properties. After that, the multiplication theorem on probability begins the discussion of independent events. You will Learn about the Bayes theorem which is categorized into smaller sections like the partition of sample space and theorem of total probability. The chapter gets over with probability distribution of random variables, mean of random variables, the variance of random variables, Bernoulli's Trials, and 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 are the benefits of solving NCERT solutions by Infinity Learn?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"NCERT solutions by Infinity Learn are designed strictly according to the latest CBSE syllabus and it is the best way to study this chapter containing all the important points and formulas. The subject matter experts designed these NCERT solutions with the aim to make the learning process the most convenient way.\"\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\": \" How can I download the NCERT Solutions of this exercise from the Infinity Learn website?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"It is very easy to download the NCERT Solutions of this exercise from the Infinity Learn website. You just have to come at Infinity Learn official website and look for the Class 12 category under the \u2018NCERT Solutions\u2019 section. After that, you can easily use these Solutions. Downloading these solutions and studying at your convenience is our main aim.\"\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 NCERT Solutions for Class 12 Maths Chapter 13, specifically in [&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 Chapter 13 Exercise 13.3","_yoast_wpseo_title":"NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.3","_yoast_wpseo_metadesc":"Simple solutions to Class 12 Maths, Chapter 13 - Probability, Exercise 13.3 from NCERT. Explained in detail for better understanding.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-13-probability-exercise-13-3\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.3<\/title>\n<meta name=\"description\" content=\"Simple solutions to Class 12 Maths, Chapter 13 - Probability, Exercise 13.3 from NCERT. 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