{"id":160460,"date":"2023-09-28T13:05:30","date_gmt":"2023-09-28T07:35:30","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=160460"},"modified":"2023-09-28T13:05:44","modified_gmt":"2023-09-28T07:35:44","slug":"a-cab-was-involved-in-a-hit-and-run-accident-at-night","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-cab-was-involved-in-a-hit-and-run-accident-at-night\/","title":{"rendered":"A cab was involved in a hit and run accident at night"},"content":{"rendered":"\n<p>Q. A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident.<\/p>\n\n\n\n<p>i. 85% of cabs in the city are green and the remaining cabs are blue.<\/p>\n\n\n\n<p>ii. A witness identified the cab involved in the accident as blue.<\/p>\n\n\n\n<p>iii. It is known that a witness can correctly identify the cab colour only 80% of the time.<\/p>\n\n\n\n<p>Which of the following options is closest to the probability that the accident was caused by a blue cab?<\/p>\n\n\n\n<p>(A) 12%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (B) 15%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (C) 41%\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (D) 80%<\/p>\n\n\n\n<p>Ans: 41%<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Probability that cab is green P(G) = 0.85<br>Probability that cab is blue P(B) = 0.15<br>Probability that witness is correct = witness identifies blue cab = P(W\/B) = 0.8<br>Probability that witness is wrong = witness identifies blue cab = P(W\/G) = 0.2<br>Probability that accident was caused by blue cab provided witness identifies it<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"343\" height=\"48\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/image-101.png\" alt=\"\" class=\"wp-image-160461\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/image-101.png 343w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/09\/image-101-300x42.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/figure>\n\n\n\n<p>Total Probability = P(W) = P(B)P(W\/B) + P(G)P(W\/G)<\/p>\n\n\n\n<p>= 0.15 \u00d7 0.8 + 0.85 \u00d7 0.2 = 1.2 + 1.7 = 2.9<\/p>\n\n\n\n<p>P(B\/W) = (0.15 \u00d7 0.8)\/2.9<br>= 1.2\/2.9 = 0.41 = 41%<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. A cab was involved in a hit and run accident at night. You are given the following data about the cabs in the city and the accident. i. 85% of cabs in the city are green and the remaining cabs are blue. ii. A witness identified the cab involved in the accident as blue. [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":160462,"comment_status":"open","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-4)","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-4)","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-4)","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":[5141],"tags":[5140],"class_list":["post-160460","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160460","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=160460"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160460\/revisions"}],"predecessor-version":[{"id":160463,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160460\/revisions\/160463"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160462"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160460"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160460"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160460"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}