{"id":1234,"date":"2021-12-17T18:03:52","date_gmt":"2021-12-17T12:33:52","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=1234"},"modified":"2022-11-19T18:43:08","modified_gmt":"2022-11-19T13:13:08","slug":"ncert-solutions-for-class-11-maths-chapter-16-probability","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-16-theory-of-probability\/","title":{"rendered":"NCERT Solutions for Class 11 Maths Chapter 16: Probability"},"content":{"rendered":"<p><span data-contrast=\"auto\">Subject specialists have created NCERT Solutions for Class 11 Maths Chapter 16 Probability, including thorough solutions for reference. All of the questions from the textbook&#8217;s exercises are answered here. Students can use these answers to help them prepare for their exams. The <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/\" target=\"_blank\" rel=\"noopener\">NCERT Solutions for Class 11<\/a><\/span><\/strong> provide useful solutions for improving conceptual knowledge.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Solutions for Class 11. Practicing these answers can be incredibly advantageous not only in exams but also in helping Class 11 pupils perform well in upcoming competitive exams.<\/span><\/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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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\">Chapter 16<br\/><\/a>\n<p><span data-contrast=\"auto\">The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management is essential for getting the best results when answering questions.<\/span><\/p>\n<p><b><span data-contrast=\"auto\">NCERT Solutions for Class 11 Maths Chapter 16 Probability<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559738&quot;:240,&quot;335559739&quot;:160,&quot;335559740&quot;:256}\"> <\/span><\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 100%;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-16-probability-exercise-16-1\/\" target=\"_blank\" rel=\"noopener\">Exercise 16.1 Solutions<\/a><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-16-probability-exercise-16-2\/\" target=\"_blank\" rel=\"noopener\">Exercise 16.2 Solutions<\/a><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-16-probability-exercise-16-3\/\" target=\"_blank\" rel=\"noopener\">Exercise 16.3 Solutions<\/a><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"width: 100%;\"><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/chapter-16-probability-miscellaneous-exercise\/\" target=\"_blank\" rel=\"noopener\">Miscellaneous Exercise Solutions<\/a><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p aria-level=\"3\"><b><span data-contrast=\"none\">NCERT Solutions for Class 11 Maths Chapter 16 Probability \u2013 Exercises<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559738&quot;:300,&quot;335559739&quot;:160,&quot;335559740&quot;:264}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The chapter Probability discusses the general applications that we encounter on a regular basis. This chapter includes three tasks and a miscellaneous activity to help students fully grasp the fundamentals of probability. Chapter 16 Probability of <strong><span style=\"color: #0000ff;\"><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-11\/maths\/\" target=\"_blank\" rel=\"noopener\">NCERT Solutions for Class 11 Maths<\/a><\/span><\/strong> covers the following major subjects and subtopics:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">16.1 &#8211; Introduction<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">This section includes a quick overview of the definition of probability and associated terminology. In basic terms, the probability is the ratio of favorable outcomes to the total number of outcomes. Experiment, sample space, occurrences, outcomes, and so on are linked concepts.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">16.2 &#8211; Random Experiments<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">16.2.1 Outcomes and sample space<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Students can easily understand the definition of a random experiment subject to the needed conditions and related terms by using examples such as tossing a coin and throwing a pair of dice.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">16.3 -Event<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-contrast=\"none\">16.3.1 Occurrence of an event<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-contrast=\"none\">16.3.2 Types of events<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-contrast=\"none\">16.3.3 Algebra of events<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-contrast=\"none\">16.3.4 Mutually exclusive events<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-contrast=\"none\">16.3.5 Exhaustive events<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">This topic has been discussed using numerous examples and experiments to thoroughly understand the terminology and types of occurrences. The intersection, union, difference, and complement of events are all explained by event algebra.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><b><span data-contrast=\"none\">16.4 &#8211; Axiomatic Approach to Probability<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-contrast=\"none\">16.4.1 Probability of an event<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-contrast=\"none\">16.4.2 Probabilities of equally likely outcomes<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-contrast=\"none\">16.4.3 Probability of the event \u2018A or B.\u2019<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p style=\"padding-left: 40px;\"><span data-contrast=\"none\">16.4.4 Probability of event \u2018not A.\u2019<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The axiomatic approach is another technique for defining the likelihood of an event. This is nicely discussed in NCERT Maths Chapter 16 for Class 11 students. There are also numerous examples and practice problems to help you grasp the idea quickly.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Following are the concepts discussed in the NCERT Solutions of Infinity Learn:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul>\n<li><span data-contrast=\"none\">Sample space is a collection of all conceivable outcomes.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">The constituents of sample space are sample points.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">An event is a subset of the sample space.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">An empty set is an impossibility event.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">Sure thing: the entire sample area.<\/span><\/li>\n<li><span data-contrast=\"none\">&#8216;Not event&#8217; or &#8216;complementary event&#8217;: The A\u2032 or S \u2013 A set.<\/span><\/li>\n<li><span data-contrast=\"none\">The set A or B: the event A or B.<\/span><\/li>\n<li><span data-contrast=\"none\">A and B: The set A and B.<\/span><\/li>\n<li><span data-contrast=\"none\">The set A \u2013 B is made up of events A and not B.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">Mutually exclusive event: If A and B are mutually exclusive, then A and B are mutually exclusive.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"none\">Events that are both exhausting and mutually exclusive.<\/span><\/li>\n<\/ul>\n<p aria-level=\"3\"><b><span data-contrast=\"none\">Following are the Key Features of NCERT Solutions for Class 11 Maths Chapter 16 Probability<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559738&quot;:300,&quot;335559739&quot;:160,&quot;335559740&quot;:264}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">Infinity Learn&#8217;s solutions to Class 11 Maths NCERT questions assist students in reinforcing their fundamentals. They also believe in enhancing their self-esteem. Students can use all of the NCERT textbook solutions for Probability in their assignments, term \u2013 II exams, and competitive exams. In addition, the information is well-structured, so students will not be able to miss any steps in their preparation.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:160,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p aria-level=\"2\"><strong>Frequently Asked Questions on NCERT Solutions for Class 11 Maths Chapter 16<\/strong><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559738&quot;:300,&quot;335559739&quot;:620,&quot;335559740&quot;:264}\"> <\/span><\/p>\n<ol>\n<li aria-level=\"2\"><span style=\"color: #ff0000;\">What is Conditional Probability in Chapter 16 of NCERT Solutions for Class 11 Maths? <\/span><\/li>\n<li aria-level=\"2\"><span style=\"color: #ff0000;\" data-contrast=\"none\">Explain a sample space covered in Chapter 16 of the NCERT Solutions for Class 11 Maths?<\/span><\/li>\n<li aria-level=\"2\"><span style=\"color: #ff0000;\" data-contrast=\"none\">List out the major topics and subtopics covered in Chapter 16 of NCERT Solutions for Class 11 Maths?<\/span><\/li>\n<\/ol>\n<p aria-level=\"3\"><strong>1. Conditional Probability in Chapter 16 of NCERT Solutions for Class 11 Maths?<\/strong><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559738&quot;:300,&quot;335559739&quot;:620,&quot;335559740&quot;:264}\"> <\/span><\/p>\n<p><span data-contrast=\"none\">The term &#8220;conditional probability&#8221; refers to a situation where an event occurs only after confirmation that the first event has already occurred. In such circumstances, the two events are unrelated to one another. As a result, the chance of event A has no bearing on the probability of event B, making event A just the probability of event B. The answers PDF describes this concept in detail to help students do well in Class 11 second term exam.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:460,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p aria-level=\"3\"><strong>2. Explain a sample space covered in Chapter 16 of the NCERT Solutions for Class 11 Maths?<\/strong><\/p>\n<p><span data-contrast=\"none\">A set contains all of the possible outcomes of a future event, such as selecting a card from many cards. It&#8217;s how you choose something from a set of samples and sample spaces. Each probability represents a small part of the sample space. As a result, the total number of choices will be one. Students can use the solutions, which are available in PDF format, to better understand this idea.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559739&quot;:460,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335559740&quot;:276}\"> <\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Subject specialists have created NCERT Solutions for Class 11 Maths Chapter 16 Probability, including thorough solutions for reference. All of [&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 11 Maths Chapter 16","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Download Free PDF of NCERT Solutions for Class 11 Maths Chapter 16: Probability solved by Expert Teachers as per NCERT (CBSE) textbook guidelines. 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