The complement of P(A\u2223B) is <\/p>\n\n\n\n
a. P(AIB). <\/p>\n\n\n\n
b. P(A C\u2223B). <\/p>\n\n\n\n
c. P(B\u2223A). <\/p>\n\n\n\n
d. P(A\u2223B C).<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To solve the problem of finding the complement of ( P(A|B) ), let\u2019s first clarify what ( P(A|B) ) represents. The notation ( P(A|B) ) stands for the conditional probability of event ( A ) occurring given that event ( B ) has occurred. Mathematically, it is defined as:<\/p>\n\n\n\n [ The complement of an event refers to the probability that the event does not occur. Therefore, the complement of ( P(A|B) ), denoted as ( P(A^c|B) ), is the probability that event ( A ) does not happen given that ( B ) has occurred. This can be mathematically expressed as:<\/p>\n\n\n\n [ Now, we need to analyze the provided options to identify which one represents ( P(A^c|B) ):<\/p>\n\n\n\n a. ( P(A|B) ): This is the probability of ( A ) given ( B ), not its complement.<\/p>\n\n\n\n b. ( P(A^c|B) ): This is indeed the correct representation of the complement of ( P(A|B) ), as it directly refers to the probability of ( A ) not occurring given ( B ).<\/p>\n\n\n\n c. ( P(B|A) ): This is the conditional probability of ( B ) given ( A ), which does not relate to the complement of ( A ) given ( B ).<\/p>\n\n\n\n d. ( P(A|B^c) ): This denotes the probability of ( A ) given that ( B ) has not occurred, which is also unrelated to the complement of ( P(A|B) ).<\/p>\n\n\n\n Thus, the correct answer is (b) ( P(A^c|B) )<\/strong>.<\/p>\n\n\n\n In conclusion, when we consider the complement of the conditional probability ( P(A|B) ), we are interested in ( P(A^c|B) ), which reflects the likelihood that ( A ) does not occur under the condition that ( B ) is true. This distinction is vital in probability theory and has implications in various fields, such as statistics, risk assessment, and decision-making. Understanding how to navigate these probabilities allows for more informed interpretations and applications in real-world scenarios.<\/p>\n","protected":false},"excerpt":{"rendered":" The complement of P(A\u2223B) is a. P(AIB). b. P(A C\u2223B). c. P(B\u2223A). d. P(A\u2223B C). The Correct Answer and Explanation is: To solve the problem of finding the complement of ( P(A|B) ), let\u2019s first clarify what ( P(A|B) ) represents. The notation ( P(A|B) ) stands for the conditional probability of event ( A […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-157519","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157519","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=157519"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/157519\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=157519"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=157519"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=157519"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
P(A|B) = \\frac{P(A \\cap B)}{P(B)}
]<\/p>\n\n\n\n
P(A^c|B) = 1 – P(A|B)
]<\/p>\n\n\n\n