{"id":7028,"date":"2021-10-22T15:40:59","date_gmt":"2021-10-22T10:10:59","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7028"},"modified":"2021-10-25T01:43:37","modified_gmt":"2021-10-24T20:13:37","slug":"a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/","title":{"rendered":"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is"},"content":{"rendered":"

Solution :<\/h2>\n

Probability of getting success, p = \\(1\\over 6\\)<\/p>\n

and probability of failure, q = \\(5\\over 6\\)<\/p>\n

Now, we must get 2 sixes in seven throws, so probability is \\(^7C_2\\)\\(({1\\over 6})^2\\)\\(({5\\over 6})^5\\)<\/p>\n

and the probability that 8th throw is \\(1\\over 6\\).<\/p>\n

\\(\\therefore\\)\u00a0 \u00a0Required Probability = \\(^7C_2\\)\\(({1\\over 6})^2\\)\\(({5\\over 6})^5\\)\\(1\\over 6\\)<\/p>\n

= \\(^7C_2\\times 5^5\\over {6^8}\\)<\/p>\n

\n

Similar Questions<\/h3>\n

The probability of India winning a test match against the west indies is 1\/2 assuming independence from match to match. The probability that in a match series India\u2019s second win occurs at the third test is<\/a><\/p>\n

Consider rolling two dice once. Calculate the probability of rolling a sum of 5 or an even sum.<\/a><\/p>\n

If A and B are two mutually exclusive events, then<\/a><\/p>\n

A and B play a game, where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is<\/a><\/p>\n

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is \\(1\\over 2\\), \\(1\\over 3\\) and \\(1\\over 4\\). Probability that the problem is solved is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Probability of getting success, p = \\(1\\over 6\\) and probability of failure, q = \\(5\\over 6\\) Now, we must get 2 sixes in seven throws, so probability is \\(^7C_2\\)\\(({1\\over 6})^2\\)\\(({5\\over 6})^5\\) and the probability that 8th throw is \\(1\\over 6\\). \\(\\therefore\\)\u00a0 \u00a0Required Probability = \\(^7C_2\\)\\(({1\\over 6})^2\\)\\(({5\\over 6})^5\\)\\(1\\over 6\\) = \\(^7C_2\\times 5^5\\over {6^8}\\) Similar …<\/p>\n

A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,44],"tags":[],"yoast_head":"\nA fair die is tossed eight times. The probability that a third six is observed on the eight throw, is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is\" \/>\n<meta property=\"og:description\" content=\"Solution : Probability of getting success, p = (1over 6) and probability of failure, q = (5over 6) Now, we must get 2 sixes in seven throws, so probability is (^7C_2)(({1over 6})^2)(({5over 6})^5) and the probability that 8th throw is (1over 6). (therefore)\u00a0 \u00a0Required Probability = (^7C_2)(({1over 6})^2)(({5over 6})^5)(1over 6) = (^7C_2times 5^5over {6^8}) Similar … A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-10-22T10:10:59+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-24T20:13:37+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is\",\"datePublished\":\"2021-10-22T10:10:59+00:00\",\"dateModified\":\"2021-10-24T20:13:37+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/\"},\"wordCount\":203,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Probability Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/\",\"url\":\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/\",\"name\":\"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-10-22T10:10:59+00:00\",\"dateModified\":\"2021-10-24T20:13:37+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/","og_locale":"en_US","og_type":"article","og_title":"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is","og_description":"Solution : Probability of getting success, p = (1over 6) and probability of failure, q = (5over 6) Now, we must get 2 sixes in seven throws, so probability is (^7C_2)(({1over 6})^2)(({5over 6})^5) and the probability that 8th throw is (1over 6). (therefore)\u00a0 \u00a0Required Probability = (^7C_2)(({1over 6})^2)(({5over 6})^5)(1over 6) = (^7C_2times 5^5over {6^8}) Similar … A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is Read More »","og_url":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/","og_site_name":"Mathemerize","article_published_time":"2021-10-22T10:10:59+00:00","article_modified_time":"2021-10-24T20:13:37+00:00","author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is","datePublished":"2021-10-22T10:10:59+00:00","dateModified":"2021-10-24T20:13:37+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/"},"wordCount":203,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Probability Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/","url":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/","name":"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-10-22T10:10:59+00:00","dateModified":"2021-10-24T20:13:37+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7028"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=7028"}],"version-history":[{"count":3,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7028\/revisions"}],"predecessor-version":[{"id":7369,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/7028\/revisions\/7369"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=7028"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=7028"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=7028"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}