{"id":1154,"date":"2023-12-19T03:33:57","date_gmt":"2023-12-19T03:33:57","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=1154"},"modified":"2023-12-26T21:37:16","modified_gmt":"2023-12-26T21:37:16","slug":"what-are-the-odds","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2023\/12\/19\/what-are-the-odds\/","title":{"rendered":"What are the odds?"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Whenever something unlikely happens, it is tempting to ask, &#8220;What are the odds?&#8221;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In some very limited cases, we can answer that question. For example, if someone deals you five cards from a well-shuffled deck, and you want to know the odds of getting a royal flush, we can answer that question <a href=\"https:\/\/en.wikipedia.org\/wiki\/Poker_probability#5-card_poker_hands\">precisely<\/a>. At least, we can if you are clearly referring to just this one hand.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">But if you&#8217;ve been playing poker regularly for a decade and then one night you are dealt a royal flush, it might not be clear, when you ask the question, whether you mean the odds of getting a royal flush on one deal, or one evening of play, or some time in your career, or once in all of the poker hands that have every been dealt. Those are different questions with very different answers &#8212; in fact, the first is close to 0 and the last is close to 1 (and known to be 1 in this universe).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, even in a highly constrained environment like a poker game, answering questions like this can be tricky. It&#8217;s even worse in real life. Say you go to college in Massachusetts and then two years later you visit Paris, go for a walk in the Tuileries Garden, and run into a friend from college. What are the odds?  Now we have to define both &#8220;in how many attempts?&#8221; and &#8220;odds of what?&#8221; Meeting this friend in this particular place? Or any old friend in any unexpected place?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now let&#8217;s put all of this thinking to the test with an example, which is the most surprising thing that has happened to me since the time I ran into a college friend in Paris. Two days ago I was working on a heat vent in my house and wanted to attach this socket<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"231\" height=\"147\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-2.png\" alt=\"\" class=\"wp-image-1155\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">to this screwdriver<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"861\" height=\"376\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-3.png\" alt=\"\" class=\"wp-image-1156\" style=\"width:567px;height:auto\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-3.png 861w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-3-300x131.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-3-768x335.png 768w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-3-604x264.png 604w\" sizes=\"auto, (max-width: 861px) 100vw, 861px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">But the socket takes a 1\/4 inch <em>square<\/em> drive, and the screwdriver takes 1\/4 inch <em>hex<\/em> bits. I figured there was probably an adapter that could connect them, but I didn&#8217;t have one. I thought about getting one, but then I found another way to do the job.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Two days later I went for a walk and about 30 yards from my house, in the middle of the street, I saw a small bit of metal that I picked up just to get it out of the way. And when I looked more closely at what is was &#8212; it was a 1\/4 inch hex to 1\/4 inch square drive adapter.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"391\" height=\"118\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-4.png\" alt=\"\" class=\"wp-image-1157\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-4.png 391w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-4-300x91.png 300w\" sizes=\"auto, (max-width: 391px) 100vw, 391px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">And here&#8217;s how it works.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"360\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-5-1024x360.png\" alt=\"\" class=\"wp-image-1158\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-5-1024x360.png 1024w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-5-300x105.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-5-768x270.png 768w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-5-604x212.png 604w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/12\/image-5.png 1108w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">So, what are the odds of that? I don&#8217;t know, but if you have a non-zero prior for the existence of a benevolent deity, you might want to update it.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Whenever something unlikely happens, it is tempting to ask, &#8220;What are the odds?&#8221; In some very limited cases, we can answer that question. For example, if someone deals you five cards from a well-shuffled deck, and you want to know the odds of getting a royal flush, we can answer that question precisely. At least, we can if you are clearly referring to just this one hand. But if you&#8217;ve been playing poker regularly for a decade and then one&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2023\/12\/19\/what-are-the-odds\/\"> Read More<span class=\"screen-reader-text\">  Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","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_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[1],"tags":[],"class_list":["post-1154","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>What are the odds? - Probably Overthinking It<\/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:\/\/www.allendowney.com\/blog\/2023\/12\/19\/what-are-the-odds\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What are the odds? - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"Whenever something unlikely happens, it is tempting to ask, &#8220;What are the odds?&#8221; In some very limited cases, we can answer that question. 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