{"id":1658,"date":"2010-05-28T21:56:29","date_gmt":"2010-05-28T20:56:29","guid":{"rendered":"http:\/\/www.decisionsciencenews.com\/?p=1658"},"modified":"2010-05-30T22:52:35","modified_gmt":"2010-05-30T21:52:35","slug":"tuesdays-child-is-full-of-probability-puzzles","status":"publish","type":"post","link":"https:\/\/www.decisionsciencenews.com\/?p=1658","title":{"rendered":"Tuesday’s child is full of probability puzzles"},"content":{"rendered":"

COUNTERINTUITIVE PROBLEM, INTUITIVE REPRESENTATION<\/p>\n

\"\"<\/a><\/p>\n

Blog posts about counterintuitive probability problems generate lots of opinions with a high probability.<\/p>\n

Andrew Gelman and readers have been having a lot of fun<\/a> with the following probability problem:<\/p>\n

I have two children. One is a boy born on a Tuesday. What is the probability I have two boys? The first thing you think is “What has Tuesday got to do with it?” Well, it has everything to do with it.<\/p><\/blockquote>\n

DSN agrees with Andrew that one virtue<\/a> of the “population-distribution” method is that it forces one to be explicit about various aspects of the problem, and in so doing, causes much confusion to disappear.<\/p>\n

As a public service this week, Decision Science News presents the population-distribution representation of the problem (what it thinks of as the Gigerenzerian \/ Hoffragian<\/a> \/ Peter Sedlmeier<\/a>-ian \"\"representation of the problem) in a visual form.<\/p>\n

To follow the logic, see Andrew’s post on how he solved the problem<\/a>. Voila:<\/p>\n

\"\"<\/a><\/p>\n

Red means “outside the reference class”. Yellow means “in the reference class but not boy-boy”. Green means “inside the reference class and boy-boy”.<\/p>\n

Boy-boy in the reference class occurs with probability Green \/ (Green + Yellow) or 13 \/27<\/p>\n

NOTE
\nTo see why DSN calls these Gigerenzerian \/ Hoffragian \/ Sedlmeierian representations, see:<\/p>\n

Sedlmeier, P. (1997). BasicBayes: A tutor system for simple Bayesian inference.
\nBehavior Research Methods, Instruments & Computers, 29(3)<\/strong>, 328-336.<\/p>\n

Gigerenzer, G., & Hoffrage, U. (1995). How to improve Bayesian reasoning without instruction: Frequency formats. Psychological Review, 102,<\/strong>, 684\u2013704.<\/p>\n

(Sorry for not using R, excel is just darn fast for some things)<\/p>\n","protected":false},"excerpt":{"rendered":"

COUNTERINTUITIVE PROBLEM, INTUITIVE REPRESENTATION Blog posts about counterintuitive probability problems generate lots of opinions with a high probability. Andrew Gelman and readers have been having a lot of fun with the following probability problem: I have two children. One is a boy born on a Tuesday. What is the probability I have two boys? The […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","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,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[4,16,74,15],"tags":[86,1208,70],"class_list":["post-1658","post","type-post","status-publish","format-standard","hentry","category-encyclopedia","category-ideas","category-r","category-tools","tag-probability","tag-r","tag-statistics"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p4LKj-qK","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/1658","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1658"}],"version-history":[{"count":11,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/1658\/revisions"}],"predecessor-version":[{"id":1888,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=\/wp\/v2\/posts\/1658\/revisions\/1888"}],"wp:attachment":[{"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1658"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1658"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.decisionsciencenews.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1658"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}