{"id":790,"date":"2012-10-10T13:17:11","date_gmt":"2012-10-10T17:17:11","guid":{"rendered":"http:\/\/efsavage.com\/blog\/?p=790"},"modified":"2012-10-10T13:17:11","modified_gmt":"2012-10-10T17:17:11","slug":"monty-hall-problem","status":"publish","type":"post","link":"https:\/\/efsavage.com\/blog\/posts\/monty-hall-problem\/","title":{"rendered":"Monty Hall Problem"},"content":{"rendered":"<p>A classic brain teaser is the <a href=\"http:\/\/en.wikipedia.org\/wiki\/Monty_Hall_problem\">Monty Hall Problem<\/a>. It fools people with a basic understanding of probability (i.e. most of us), and even after a good amount of consternation seems unintuitive. If complex mathematical formulas don&#8217;t convince you, then you&#8217;ll likely have to see it actually happen to believe it, as I did.<\/p>\n<p>I came across it again today, and I was unhappy with the idea that this remained a difficult hurdle for my brain to jump, even though at this point I know the answer. \u00a0I came up with the following explanation that I think is as simple as it gets, so if it still sticks in your craw as it did mine, perhaps this will help.<\/p>\n<p>If you never switch:<\/p>\n<ul>\n<li>1\/3 of time you pick right door, and win.<\/li>\n<li>2\/3 of time you pick wrong door, and lose.<\/li>\n<\/ul>\n<p>(1\/3 * 1) + (2\/3 * 0) = 1\/3<\/p>\n<p>So if you never switch, you will win 1\/3 of the time.<\/p>\n<p>If you always switch:<\/p>\n<ul>\n<li>1\/3 of time you pick right door, Monty will open either of the empty doors, and then you will open the other empty door, and lose.<\/li>\n<li>2\/3 of time you pick an empty door, Monty will open <strong>the other empty door<\/strong>, and then you will open the door with the prize and win.<\/li>\n<\/ul>\n<p>(1\/3 * 0) + (2\/3 * 1) = 2\/3<\/p>\n<p>If you always switch, you will win 2\/3 of the time.<\/p>\n<p>Diagrams and formulas aside, the phrase &#8220;the other empty door&#8221; is what made it come together for me.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A classic brain teaser is the Monty Hall Problem. It fools people with a basic understanding of probability (i.e. most of us), and even after a good amount of consternation seems unintuitive. If complex mathematical formulas don&#8217;t convince you, then you&#8217;ll likely have to see it actually happen to believe it, as I did. I&hellip; <\/p>\n<p class=\"simppeli-read-more\"><a href=\"https:\/\/efsavage.com\/blog\/posts\/monty-hall-problem\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Monty Hall Problem<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[41],"tags":[374,373],"series":[],"class_list":["post-790","post","type-post","status-publish","format-standard","hentry","category-random","tag-math","tag-probability"],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p1AkJt-cK","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/posts\/790","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/comments?post=790"}],"version-history":[{"count":2,"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/posts\/790\/revisions"}],"predecessor-version":[{"id":798,"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/posts\/790\/revisions\/798"}],"wp:attachment":[{"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/media?parent=790"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/categories?post=790"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/tags?post=790"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/efsavage.com\/blog\/wp-json\/wp\/v2\/series?post=790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}