{"id":243,"date":"2023-09-19T06:23:43","date_gmt":"2023-09-19T06:23:43","guid":{"rendered":"http:\/\/bullseye.ac\/blog\/?p=243"},"modified":"2023-09-19T06:23:43","modified_gmt":"2023-09-19T06:23:43","slug":"the-two-daughter-problem","status":"publish","type":"post","link":"https:\/\/bullseye.ac\/blog\/sciences\/the-drunkards-walk-how-randomness-rules-our-lives-by-leonard-mlodinow\/the-two-daughter-problem\/","title":{"rendered":"The Two Daughter Problem"},"content":{"rendered":"\n<p>In the two-daughter problem, an additional question is usually asked: What are the chances, <em>given that one of the children is a girl, <\/em>that both children will be girls? One might reason this way: since it is given that one of the children is a girl, there is only one child left to look at. The chance of that child\u2019s being a girl is 50 percent, so the probability that both children are girls is 50 percent.<\/p>\n\n\n\n<p>That is not correct. Why? Although the statement of the problem says that one child is a girl, it doesn\u2019t say <em>which <\/em>one, and that changes things. If that sounds confusing, that\u2019s okay, because it provides a good illustration of the power of Cardano\u2019s method, which makes the reasoning clear.<\/p>\n\n\n\n<p>The new information\u2014one of the children is a girl\u2014means that we are eliminating from consideration the possibility that both children are boys. And so, employing Cardano\u2019s approach, we eliminate the possible outcome (boy, boy) from the sample space. That leaves only 3 outcomes in the sample space: (girl, boy), (boy, girl), and (girl, girl). Of these, only (girl, girl) is the favorable outcome\u2014that is, both children are daughters\u2014so the chances that both children are girls is 1 in 3, or 33 percent. Now we can see why it matters that the statement of the problem didn\u2019t specify which child was a daughter. For instance, if the problem had asked for the chances of both children being girls <em>given that the first child is a girl, <\/em>then we would have eliminated both (boy, boy) and (boy, girl) from the sample space and the odds would have been 1 in 2, or 50 percent.<\/p>\n\n\n\n<p><em>Excerpted from &#8216;The Drunkard&#8217;s Walk &#8211; How Randomness Rules our Lives&#8217; by Leonard Mlodinow<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In the two-daughter problem, an additional question is usually asked: What are the chances, given that one of the children is a girl, that both children will be girls? One might reason this way: since it is given that one of the children is a girl, there is only one child left to look at. &#8230; <a title=\"The Two Daughter Problem\" class=\"read-more\" href=\"https:\/\/bullseye.ac\/blog\/sciences\/the-drunkards-walk-how-randomness-rules-our-lives-by-leonard-mlodinow\/the-two-daughter-problem\/\" aria-label=\"More on The Two Daughter Problem\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_eb_attr":"","_uag_custom_page_level_css":"","footnotes":""},"categories":[25],"tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>The Two Daughter Problem - BullsEye<\/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:\/\/bullseye.ac\/blog\/sciences\/the-drunkards-walk-how-randomness-rules-our-lives-by-leonard-mlodinow\/the-two-daughter-problem\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The Two Daughter Problem - BullsEye\" \/>\n<meta property=\"og:description\" content=\"In the two-daughter problem, an additional question is usually asked: What are the chances, given that one of the children is a girl, that both children will be girls? 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