{"id":426,"date":"2020-01-28T17:49:27","date_gmt":"2020-01-28T17:49:27","guid":{"rendered":"https:\/\/www.allendowney.com\/blog\/?p=426"},"modified":"2020-01-28T17:49:27","modified_gmt":"2020-01-28T17:49:27","slug":"the-elvis-problem-revisited","status":"publish","type":"post","link":"https:\/\/www.allendowney.com\/blog\/2020\/01\/28\/the-elvis-problem-revisited\/","title":{"rendered":"The Elvis problem revisited"},"content":{"rendered":"\n<p>Here&#8217;s a problem from <a href=\"https:\/\/amzn.to\/3aPoNjQ\">Bayesian Data Analysis<\/a>:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin?<\/p><\/blockquote>\n\n\n\n<p>I will answer this question in three steps:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>First, we need some background information about the relative frequencies of identical and fraternal twins.<\/li><li>Then we will use Bayes&#8217;s Theorem to take into account one piece of data, which is that Elvis&#8217;s twin was male.<\/li><li>Finally, living up to the name of this blog, I will overthink the problem by taking into account a second piece of data, which is that Elvis&#8217;s twin died at birth.<\/li><\/ul>\n\n\n\n<p>For background information, I&#8217;ll use data from 1935, the year Elvis was born, from the U.S. Census Bureau, <a href=\"https:\/\/www.cdc.gov\/nchs\/data\/vsushistorical\/birthstat_1935.pdf\">Birth, Stillbirth, and Infant Mortality Statistics for the Continental United States, the Territory of Hawaii, the Virgin Islands 1935<\/a>.<\/p>\n\n\n\n<p>It includes this table:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"593\" src=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/01\/birth_data_1935.png\" alt=\"\" class=\"wp-image-427\" srcset=\"https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/01\/birth_data_1935.png 600w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/01\/birth_data_1935-300x297.png 300w, https:\/\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/01\/birth_data_1935-273x270.png 273w\" sizes=\"auto, (max-width: 600px) 100vw, 600px\" \/><\/figure>\n\n\n\n<p>With a few reasonable assumptions, we can use this data to compute the probability that Elvis was an identical twin, given that his twin brother died at birth.<\/p>\n\n\n\n<p><a href=\"https:\/\/colab.research.google.com\/github\/AllenDowney\/BiteSizeBayes\/blob\/master\/elvis.ipynb\">You can see my solution in this Jupyter notebook.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here&#8217;s a problem from Bayesian Data Analysis: Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin? I will answer this question in three steps: First, we need some background information about the relative frequencies of identical and fraternal twins. Then we will use Bayes&#8217;s Theorem to take into account one piece of data, which is that Elvis&#8217;s twin was male. Finally, living up to the name of this blog,&#8230;<\/p>\n<p class=\"read-more\"><a class=\"btn btn-default\" href=\"https:\/\/www.allendowney.com\/blog\/2020\/01\/28\/the-elvis-problem-revisited\/\"> 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_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":[64],"class_list":["post-426","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-elvis"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The Elvis problem revisited - 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\/2020\/01\/28\/the-elvis-problem-revisited\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Elvis problem revisited - Probably Overthinking It\" \/>\n<meta property=\"og:description\" content=\"Here&#8217;s a problem from Bayesian Data Analysis: Elvis Presley had a twin brother (who died at birth). What is the probability that Elvis was an identical twin? I will answer this question in three steps: First, we need some background information about the relative frequencies of identical and fraternal twins. Then we will use Bayes&#8217;s Theorem to take into account one piece of data, which is that Elvis&#8217;s twin was male. Finally, living up to the name of this blog,... 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Each line\u2026","rel":"","context":"In \"age period cohort analysis\"","block_context":{"text":"age period cohort analysis","link":"https:\/\/www.allendowney.com\/blog\/tag\/age-period-cohort-analysis\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/03\/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/03\/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/03\/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/03\/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2026\/03\/cohort_standardized_-2dbe3fdd869f5be03f0b91d2cf3b980e.png?resize=1050%2C600&ssl=1 3x"},"classes":[]},{"id":1286,"url":"https:\/\/www.allendowney.com\/blog\/2024\/05\/20\/bertrands-boxes\/","url_meta":{"origin":426,"position":1},"title":"Bertrand\u2019s Boxes","author":"AllenDowney","date":"May 20, 2024","format":false,"excerpt":"An early draft of Probably Overthinking It included two chapters about probability. 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Here's an excerpt from the\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":498,"url":"https:\/\/www.allendowney.com\/blog\/2020\/10\/21\/millennials-are-not-getting-married\/","url_meta":{"origin":426,"position":2},"title":"Millennials are not getting married","author":"AllenDowney","date":"October 21, 2020","format":false,"excerpt":"In 2015 I wrote a paper called \"Will Millennials Ever Get Married?\" where I used data from the National Survey of Family Growth (NSFG) to estimate the age at first marriage for women in the U.S, broken down by decade of birth. \u00a0 I found that women born in the\u2026","rel":"","context":"In \"marriage\"","block_context":{"text":"marriage","link":"https:\/\/www.allendowney.com\/blog\/tag\/marriage\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/10\/marriage4-3.png?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/10\/marriage4-3.png?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/10\/marriage4-3.png?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/10\/marriage4-3.png?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/10\/marriage4-3.png?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2020\/10\/marriage4-3.png?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":1715,"url":"https:\/\/www.allendowney.com\/blog\/2026\/01\/31\/the-girl-born-on-tuesday\/","url_meta":{"origin":426,"position":3},"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? 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But I was not satisfied with my solution or the way I explained it, so I cut it from the second edition. I am\u2026","rel":"","context":"In \"bayesian statistics\"","block_context":{"text":"bayesian statistics","link":"https:\/\/www.allendowney.com\/blog\/tag\/bayesian-statistics\/"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/github.com\/AllenDowney\/ThinkBayes2\/raw\/master\/examples\/jaynes177.png?resize=350%2C200&ssl=1","width":350,"height":200},"classes":[]},{"id":1097,"url":"https:\/\/www.allendowney.com\/blog\/2023\/11\/07\/we-have-a-book\/","url_meta":{"origin":426,"position":5},"title":"We Have a Book!","author":"AllenDowney","date":"November 7, 2023","format":false,"excerpt":"My copy of Probably Overthinking It has arrived! If you want a copy for yourself, you can get a 30% discount if you order from the publisher and use the code UCPNEW. You can also order from Amazon or, if you want to support independent bookstores, from Bookshop.org. The official\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\/2023\/11\/IMG_20231107_104338_7.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.allendowney.com\/blog\/wp-content\/uploads\/2023\/11\/IMG_20231107_104338_7.jpg?resize=1400%2C800&ssl=1 4x"},"classes":[]}],"_links":{"self":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/426","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=426"}],"version-history":[{"count":3,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/426\/revisions"}],"predecessor-version":[{"id":430,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/posts\/426\/revisions\/430"}],"wp:attachment":[{"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/media?parent=426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/categories?post=426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.allendowney.com\/blog\/wp-json\/wp\/v2\/tags?post=426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}