{"id":656,"date":"2021-07-23T15:36:20","date_gmt":"2021-07-23T15:36:20","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=656"},"modified":"2025-09-16T21:13:29","modified_gmt":"2025-09-16T21:13:29","slug":"the-left-handed-sister-problem","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2021\/07\/23\/the-left-handed-sister-problem\/","title":{"rendered":"The Left-Handed Sister Problem"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Suppose you meet someone who looks like the brother of your friend Mary. You ask if he has a sister named Mary, and he says &#8220;Yes I do, but I don&#8217;t think I know you.&#8221;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">You remember that Mary has a sister who is left-handed, but you don&#8217;t remember her name. So you ask your new friend if he has another sister who is left-handed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If he does, how much evidence does that provide that he is the brother of your friend, rather than a random person who coincidentally has a sister named Mary and another sister who is left-handed? In other words, what is the Bayes factor of the left-handed sister?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s assume:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Out of 100 families with children, 20 have one child, 30 have two children, 40 have three children, and 10 have four children.<\/li>\n\n\n\n<li>All children are either boys or girls with equal probability, one girl in 10 is left-handed, and one girl in 100 is named Mary.<\/li>\n\n\n\n<li>Name, sex, and handedness are independent, so every child has the same probability of being a girl, left-handed, or named Mary.<\/li>\n\n\n\n<li>If the person you met had more than one sister named Mary, he would have said so, but he could have more than one sister who is left handed.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">I&#8217;ll post a solution only when someone <a href=\"https:\/\/twitter.com\/AllenDowney\/status\/1418596609647120389\" target=\"_blank\" rel=\"noreferrer noopener\">replies to this tweet<\/a> with a correct answer!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">UPDATE: <a href=\"https:\/\/allendowney.github.io\/ThinkBayes2\/sister.html\">Here it is<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you like this sort of thing, you might like the <a href=\"https:\/\/amzn.to\/334eqGo\" target=\"_blank\" rel=\"noreferrer noopener\">new second edition of <em>Think Bayes<\/em><\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Suppose you meet someone who looks like the brother of your friend Mary. You ask if he has a sister named Mary, and he says &#8220;Yes I do, but I don&#8217;t think I know you.&#8221; You remember that Mary has a sister who is left-handed, but you don&#8217;t remember her name. So you ask your new friend if he has another sister who is left-handed. If he does, how much evidence does that provide that he is the brother of&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2021\/07\/23\/the-left-handed-sister-problem\/\"> 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_hide_featured_image":false,"_jetpack_featured_image_duplicate_dismissed":0,"_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":[63],"class_list":["post-656","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-bayess-theorem"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.7 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>The Left-Handed Sister Problem - 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\/2021\/07\/23\/the-left-handed-sister-problem\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Left-Handed Sister Problem - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"Suppose you meet someone who looks like the brother of your friend Mary. You ask if he has a sister named Mary, and he says &#8220;Yes I do, but I don&#8217;t think I know you.&#8221; You remember that Mary has a sister who is left-handed, but you don&#8217;t remember her name. So you ask your new friend if he has another sister who is left-handed. If he does, how much evidence does that provide that he is the brother of... Read More Read More\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.allendowney.com\/blog\/2021\/07\/23\/the-left-handed-sister-problem\/\" \/>\n<meta property=\"og:site_name\" content=\"Probably Overthinking It\" \/>\n<meta property=\"article:published_time\" content=\"2021-07-23T15:36:20+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-09-16T21:13:29+00:00\" \/>\n<meta name=\"author\" content=\"Allen B. Downey\" \/>\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=\"Allen B. Downey\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2021\\\/07\\\/23\\\/the-left-handed-sister-problem\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/www.allendowney.com\\\/blog\\\/2021\\\/07\\\/23\\\/the-left-handed-sister-problem\\\/\"},\"author\":{\"name\":\"Allen B. 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