{"id":138,"date":"2026-04-11T15:23:11","date_gmt":"2026-04-11T09:53:11","guid":{"rendered":"https:\/\/gsama.cc\/?p=138"},"modified":"2026-04-11T15:23:12","modified_gmt":"2026-04-11T09:53:12","slug":"last-child-lie","status":"publish","type":"post","link":"https:\/\/gsama.cc\/?p=138","title":{"rendered":"last child lie"},"content":{"rendered":"\n<p>It is been commonly reported by the media that India\u2019s skewed gender ratio\u2014roughly 950 girls to 1000 boys\u2014is caused by the &#8220;stopping rule&#8221; (families having children until a son is born, then stopping). <\/p>\n\n\n\n<p>This results in a 1-child family will always be a son, and a 4-child family will have three daughters and a son. Then will there be more sons or more daughters? <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Thought Experiment<\/h3>\n\n\n\n<p>Imagine 1,000 couples who only stop once they have a boy. <\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Round 1<\/strong>: 1,000 babies are born. \n<ul class=\"wp-block-list\">\n<li>Statistically: 500 Boys, 500 Girls.<\/li>\n\n\n\n<li>The 500 parents of boys stop. <\/li>\n\n\n\n<li>The 500 parents of girls try again.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Round 2<\/strong>: 500 babies are born. \n<ul class=\"wp-block-list\">\n<li>Statistically: 250 Boys, 250 Girls.<\/li>\n\n\n\n<li>The 250 parents of boys stop. <\/li>\n\n\n\n<li>The 250 parents of girls try again.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Round 3<\/strong>: 250 babies are born. \n<ul class=\"wp-block-list\">\n<li>Statistically: 125 Boys, 125 Girls.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p>No matter how many rounds you play, the number of boys born in each round always equals the number of girls.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Independent Event Principle<\/h3>\n\n\n\n<p>The math holds because each birth is an independent event. Nature has no memory; the probability of a boy or girl is always 0.5 for every single birth, regardless of what came before.<\/p>\n\n\n\n<div class=\"wp-block-math\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>b<\/mi><mi>o<\/mi><mi>y<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>P<\/mi><mo form=\"prefix\" stretchy=\"false\">(<\/mo><mi>g<\/mi><mi>i<\/mi><mi>r<\/mi><mi>l<\/mi><mo form=\"postfix\" stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0.5<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(boy) = P(girl) = 0.5<\/annotation><\/semantics><\/math><\/div>\n\n\n\n<p> &#8220;stopping rule&#8221; decides the number of births, but it cannot change the probability of those births. <\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Mathematically, if you let nature take its course, &#8220;stopping after a boy&#8221; will always result in a 1:1 ratio. The observed skew in the population is a result of <em>human intervention<\/em>\u2014where the &#8220;coin flip&#8221; itself is manipulated\u2014not the statistical outcome of stopping rules.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is been commonly reported by the media that India\u2019s skewed gender ratio\u2014roughly 950 girls to 1000 boys\u2014is caused by the &#8220;stopping rule&#8221; (families having children until a son is born, then stopping). This results in a 1-child family will always be a son, and a 4-child family will have three daughters and a son. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-138","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/posts\/138","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gsama.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=138"}],"version-history":[{"count":1,"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/posts\/138\/revisions"}],"predecessor-version":[{"id":139,"href":"https:\/\/gsama.cc\/index.php?rest_route=\/wp\/v2\/posts\/138\/revisions\/139"}],"wp:attachment":[{"href":"https:\/\/gsama.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=138"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gsama.cc\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=138"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gsama.cc\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=138"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}