{"id":94,"date":"2018-12-03T14:04:34","date_gmt":"2018-12-03T14:04:34","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=94"},"modified":"2018-12-03T14:04:34","modified_gmt":"2018-12-03T14:04:34","slug":"lions-and-tigers-and-bears","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/","title":{"rendered":"Lions and tigers and bears"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignright\" src=\"http:\/\/mfsaweb.org\/wp-content\/uploads\/WizardOfOz.jpg\" width=\"323\" height=\"242\" \/>Here&#8217;s another Bayes puzzle:<\/p>\n<p><em>Suppose we visit a wild animal preserve where we know that the only animals are lions and tigers and bears, but we don&#8217;t know how many of each there are.<\/em><\/p>\n<p><em>During the tour, we see 3 lions, 2 tigers,\u00a0and one bear. Assuming that every animal had an equal chance to appear in our sample, estimate the prevalence of each species.<\/em><\/p>\n<p><em>What is the probability that the next animal we see is a bear?<\/em><\/p>\n<h3>Solutions<\/h3>\n<div class=\"oembed-gist\"><script src=\"https:\/\/gist.github.com\/AllenDowney\/8b198f4ee59b5f8ffa9be90963f618a5.js\"><\/script><noscript>View the code on <a href=\"https:\/\/gist.github.com\/AllenDowney\/8b198f4ee59b5f8ffa9be90963f618a5\">Gist<\/a>.<\/noscript><\/div>\n<p><a href=\"http:\/\/nbviewer.jupyter.org\/github\/WillKoehrsen\/probabilistic-programming\/blob\/master\/Allen%20Downey%20Problem.ipynb\">Will Koehrsen posted an excellent solution here<\/a>.\u00a0 His solution is more general than mine, allowing for uncertainty about the parameters of the Dirichlet prior.<\/p>\n<p>And vlad<a href=\"https:\/\/gist.github.com\/usptact\/263f63f0af1bc41fb7d7ddc7e5e6123c\">\u00a0posted another good solution using WebPPL<\/a>.<\/p>\n<p>&nbsp;<\/p>\n<h3>Cats and rats and elephants<\/h3>\n<p>Now that we solved the appetizer, we are ready for the main course&#8230;<\/p>\n<p><em>Suppose there are six species that might be in a zoo: lions and tigers and bears, and cats and rats and elephants.\u00a0 Every zoo has a subset of these species, and every subset is equally likely.<\/em><\/p>\n<p><em>One day we visit a zoo and see\u00a03 lions, 2 tigers,\u00a0and one bear.\u00a0 Assuming that every animal in the zoo has an equal chance to be seen, what is the probability that the next animal we see is an elephant?<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here&#8217;s another Bayes puzzle: Suppose we visit a wild animal preserve where we know that the only animals are lions and tigers and bears, but we don&#8217;t know how many of each there are. During the tour, we see 3 lions, 2 tigers,\u00a0and one bear. Assuming that every animal had an equal chance to appear in our sample, estimate the prevalence of each species. What is the probability that the next animal we see is a bear? Solutions View the&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/\"> Read More<span class=\"screen-reader-text\">  Read More<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_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":"","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}},"categories":[1],"tags":[],"class_list":["post-94","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Lions and tigers and bears - 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\/2018\/12\/03\/lions-and-tigers-and-bears\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Lions and tigers and bears - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"Here&#8217;s another Bayes puzzle: Suppose we visit a wild animal preserve where we know that the only animals are lions and tigers and bears, but we don&#8217;t know how many of each there are. During the tour, we see 3 lions, 2 tigers,\u00a0and one bear. Assuming that every animal had an equal chance to appear in our sample, estimate the prevalence of each species. What is the probability that the next animal we see is a bear? Solutions View the... Read More Read More\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/\" \/>\n<meta property=\"og:site_name\" content=\"Probably Overthinking It\" \/>\n<meta property=\"article:published_time\" content=\"2018-12-03T14:04:34+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/mfsaweb.org\/wp-content\/uploads\/WizardOfOz.jpg\" \/>\n<meta name=\"author\" content=\"AllenDowney\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@AllenDowney\" \/>\n<meta name=\"twitter:site\" content=\"@AllenDowney\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"AllenDowney\" \/>\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:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/\"},\"author\":{\"name\":\"AllenDowney\",\"@id\":\"https:\/\/www.allendowney.com\/blog\/#\/schema\/person\/4e5bfb2e9af6c3446cb0031a7bf83207\"},\"headline\":\"Lions and tigers and bears\",\"datePublished\":\"2018-12-03T14:04:34+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/\"},\"wordCount\":225,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/www.allendowney.com\/blog\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/#primaryimage\"},\"thumbnailUrl\":\"http:\/\/mfsaweb.org\/wp-content\/uploads\/WizardOfOz.jpg\",\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/\",\"url\":\"https:\/\/www.allendowney.com\/blog\/2018\/12\/03\/lions-and-tigers-and-bears\/\",\"name\":\"Lions and tigers and bears - 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Now here's the follow-up question: Suppose there are six species that might be in a zoo: lions\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"Wall decoration featuring an elephant.","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2018\/12\/pexels-photo-1368496-300x300.jpeg?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":80,"url":"https:\/\/www.allendowney.com\/blog\/2018\/10\/21\/the-game-of-ur-problem\/","url_meta":{"origin":94,"position":1},"title":"The Game of Ur problem","author":"AllenDowney","date":"October 21, 2018","format":false,"excerpt":"Here's a probability puzzle to ruin your week. In the Royal Game of Ur, players advance tokens along a track with 14 spaces. To determine how many spaces to advance, a player rolls 4 dice with 4 sides. 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What is the probability that they are male? 2) Suppose I choose two U.S. residents at random and A is taller than\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":1255,"url":"https:\/\/www.allendowney.com\/blog\/2024\/03\/08\/think-python-goes-to-production\/","url_meta":{"origin":94,"position":3},"title":"Think Python Goes to Production","author":"AllenDowney","date":"March 8, 2024","format":false,"excerpt":"Think Python has moved into production, on schedule for the official publication date in July -- but maybe earlier if things go well. To celebrate, I have posted the next batch of chapters on the new site, up through Chapter 12, which is about Markov text analysis and generation, one\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2024\/03\/Think_Python_3e_cover.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1715,"url":"https:\/\/www.allendowney.com\/blog\/2026\/01\/31\/the-girl-born-on-tuesday\/","url_meta":{"origin":94,"position":4},"title":"The Girl Born on Tuesday","author":"AllenDowney","date":"January 31, 2026","format":false,"excerpt":"Some people have strong opinions about this question: In a family with two children, if at least one of the children is a girl born on Tuesday, what are the chances that both children are girls? In this article, I hope to offer A solution to one interpretation of this\u2026","rel":"","context":"In \"Bayes&#039;s Theorem\"","block_context":{"text":"Bayes&#039;s Theorem","link":"https:\/\/www.allendowney.com\/blog\/tag\/bayess-theorem\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/01\/c81aa262e67d9b56ecabe5664c2397cdd0375ce23e2d2c683d8d281e36c47726.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/01\/c81aa262e67d9b56ecabe5664c2397cdd0375ce23e2d2c683d8d281e36c47726.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/01\/c81aa262e67d9b56ecabe5664c2397cdd0375ce23e2d2c683d8d281e36c47726.png?resize=525%2C300&ssl=1 1.5x"},"classes":[]},{"id":902,"url":"https:\/\/www.allendowney.com\/blog\/2023\/04\/02\/llm-assisted-programming\/","url_meta":{"origin":94,"position":5},"title":"LLM-Assisted Programming","author":"AllenDowney","date":"April 2, 2023","format":false,"excerpt":"I've been experimenting with programming assisted by Large Language Models (LLMs) like ChatGPT. I am amazed at how good it is, and it seems clear to me that the great majority of programming work will be LLM-assisted, starting now. Here are some of the examples I've tried. Think Python For\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"_links":{"self":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/94","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/comments?post=94"}],"version-history":[{"count":1,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/94\/revisions"}],"predecessor-version":[{"id":95,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/94\/revisions\/95"}],"wp:attachment":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/media?parent=94"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/categories?post=94"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/tags?post=94"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}