{"id":160343,"date":"2023-09-26T13:26:25","date_gmt":"2023-09-26T07:56:25","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=160343"},"modified":"2023-09-26T13:26:25","modified_gmt":"2023-09-26T07:56:25","slug":"consider-guwahati-g-and-delhi-d-whose-temperatures-can-be-classified-as-high-%f0%9d%90%bb-medium-%f0%9d%91%80-and-low-%f0%9d%90%bf","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/consider-guwahati-g-and-delhi-d-whose-temperatures-can-be-classified-as-high-%f0%9d%90%bb-medium-%f0%9d%91%80-and-low-%f0%9d%90%bf\/","title":{"rendered":"Consider Guwahati (G) and Delhi (D) whose temperatures can be classified as high (\ud835\udc3b), medium (\ud835\udc40) and low (\ud835\udc3f)"},"content":{"rendered":"\n

Q. Consider Guwahati (G) and Delhi (D) whose temperatures can be classified as high (\ud835\udc3b), medium (\ud835\udc40) and low (\ud835\udc3f). Let \ud835\udc43(\ud835\udc3b\ud835\udc3a<\/sub>) denote the probability that Guwahati has high temperature. Similarly, \ud835\udc43(\ud835\udc40\ud835\udc3a<\/sub>) and \ud835\udc43(\ud835\udc3f\ud835\udc3a<\/sub>) denotes the probability of Guwahati having medium and low temperatures respectively. Similarly, we use \ud835\udc43(\ud835\udc3b\ud835\udc37<\/sub>), \ud835\udc43(\ud835\udc40\ud835\udc37<\/sub>) and \ud835\udc43(\ud835\udc3f\ud835\udc37<\/sub>) for Delhi.<\/p>\n\n\n\n

The following table gives the conditional probabilities for Delhi\u2019s temperature given Guwahati\u2019s temperature.<\/p>\n\n\n\n

 <\/td>\ud835\udc3b\ud835\udc37<\/sub><\/td>\ud835\udc40\ud835\udc37<\/sub><\/td>\ud835\udc3f\ud835\udc37<\/sub><\/td><\/tr>
\ud835\udc3b\ud835\udc3a<\/sub><\/td>0.40<\/td>0.48<\/td>0.12<\/td><\/tr>
\ud835\udc40\ud835\udc3a<\/sub><\/td>0.10<\/td>0.65<\/td>0.25<\/td><\/tr>
\ud835\udc3f\ud835\udc3a<\/sub><\/td>0.01<\/td>0.50<\/td>0.49<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

Consider the first row in the table above. The first entry denotes that if Guwahati has high temperature (\ud835\udc3b\ud835\udc3a<\/sub>) then the probability of Delhi also having a high temperature (\ud835\udc3b\ud835\udc37<\/sub>) is 0.40; i.e., \ud835\udc43(\ud835\udc3b\ud835\udc37<\/sub>|\ud835\udc3b\ud835\udc3a<\/sub>) = 0.40. Similarly, the next two entries are \ud835\udc43(\ud835\udc40\ud835\udc37<\/sub>|\ud835\udc3b\ud835\udc3a<\/sub>) = 0.48 and \ud835\udc43(\ud835\udc3f\ud835\udc37<\/sub>|\ud835\udc3b\ud835\udc3a<\/sub>) = 0.12. Similarly for the other rows.<\/p>\n\n\n\n

If it is known that \ud835\udc43(\ud835\udc3b\ud835\udc3a<\/sub>) = 0.2, \ud835\udc43(\ud835\udc40\ud835\udc3a<\/sub>) = 0.5, and \ud835\udc43(\ud835\udc3f\ud835\udc3a<\/sub>) = 0.3, then the probability (correct to two decimal places) that Guwahati has high temperature given that Delhi has high temperature is\u00a0<\/p>\n\n\n\n

Ans: 0.6015<\/p>\n\n\n\n

Sol:<\/p>\n\n\n\n

P(HD<\/sub>) = P(HD<\/sub> \u2223 HG<\/sub>) \u00d7 P(HG<\/sub>) + P(HD<\/sub> \u2223 MG<\/sub>) \u00d7 P(MG<\/sub>) + P(HD<\/sub> \u2223 LG<\/sub>) \u00d7 P(LG<\/sub>)
P(HD<\/sub>) = 0.4 \u00d7 0.2 + 0.1 \u00d7 0.5 + 0.01 \u00d7 0.3 = 0.133<\/p>\n\n\n\n

Therefore,
P(HG<\/sub> \u2223 HD<\/sub>) = P(HG<\/sub> \u2229 HD<\/sub>) \/ P(HD<\/sub>)
P(HG<\/sub> \u2223 HD<\/sub>) = P(HD<\/sub> \u2223 HG<\/sub>) \u00d7 P(HG<\/sub>) \/ P(HD<\/sub>)
P(HG<\/sub> \u2223 HD<\/sub>) = 0.40 \u00d7 0.2 \/ P(HD<\/sub>) = 0.08 \/ 0.133 = 0.6015<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"

Q. Consider Guwahati (G) and Delhi (D) whose temperatures can be classified as high (\ud835\udc3b), medium (\ud835\udc40) and low (\ud835\udc3f). Let \ud835\udc43(\ud835\udc3b\ud835\udc3a) denote the probability that Guwahati has high temperature. Similarly, \ud835\udc43(\ud835\udc40\ud835\udc3a) and \ud835\udc43(\ud835\udc3f\ud835\udc3a) denotes the probability of Guwahati having medium and low temperatures respectively. Similarly, we use \ud835\udc43(\ud835\udc3b\ud835\udc37), \ud835\udc43(\ud835\udc40\ud835\udc37) and \ud835\udc43(\ud835\udc3f\ud835\udc37) for Delhi. The […]<\/p>\n","protected":false},"author":419,"featured_media":160344,"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-160343","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\/160343","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=160343"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160343\/revisions"}],"predecessor-version":[{"id":160345,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160343\/revisions\/160345"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160344"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160343"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160343"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160343"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}