{"id":193,"date":"2022-01-19T05:56:33","date_gmt":"2022-01-19T05:56:33","guid":{"rendered":"https:\/\/qpr.ca\/blogs\/mathstuff\/?p=193"},"modified":"2022-01-19T06:00:27","modified_gmt":"2022-01-19T06:00:27","slug":"3-alan-coopers-answer-to-question-a-bar-of-length-%e2%84%93-is-broken-into-three-pieces-at-two-random-spots-what-is-the-probability-that-the-length-of-at-least-one-piece-is-less-than-%e2%84%93-2","status":"publish","type":"post","link":"https:\/\/qpr.ca\/blogs\/mathstuff\/2022\/01\/19\/3-alan-coopers-answer-to-question-a-bar-of-length-%e2%84%93-is-broken-into-three-pieces-at-two-random-spots-what-is-the-probability-that-the-length-of-at-least-one-piece-is-less-than-%e2%84%93-2\/","title":{"rendered":"(3) Alan Cooper’s answer to Question: A bar of length \u2113 is broken into three pieces at two random spots. What is the probability that the length of at least one piece is less than \u2113\/20? Can anyone hlp me? Thks a lot – Quora"},"content":{"rendered":"

The question is ill-posed because there are many different ways of choosing two spots \u201cat random\u201d. BUT if we assume that the cuts are made independently with each chosen according to a uniform probability per unit length then the answer is the fraction of the big square that is not shaded in the diagram below . (ie p = 1-(17\/20)^2)<\/p>\n

\"\"<\/p>\n

Source: (3) Alan Cooper’s answer to Question: A bar of length \u2113 is broken into three pieces at two random spots. What is the probability that the length of at least one piece is less than \u2113\/20? Can anyone hlp me? Thks a lot – Quora<\/a><\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

The question is ill-posed because there are many different ways of choosing two spots \u201cat random\u201d. BUT if we assume that the cuts are made independently with each chosen according to a uniform probability per unit length then the answer is the fraction of the big square that is not shaded in the diagram below…<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-193","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/posts\/193","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/comments?post=193"}],"version-history":[{"count":2,"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/posts\/193\/revisions"}],"predecessor-version":[{"id":197,"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/posts\/193\/revisions\/197"}],"wp:attachment":[{"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/media?parent=193"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/categories?post=193"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/qpr.ca\/blogs\/mathstuff\/wp-json\/wp\/v2\/tags?post=193"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}