I saw an ad on TV yesterday that made me think about statistics. It featured a shot of three women, with voice over saying “1 in three women develop disease X” (can’t remember what it was). The implication, of course, is that one of the three women shown in the picture will develop disease X. You’re supposed to be thinking “which one will it be”. This is vaguely reminiscent of my first class at university where a lecturer told us to look left and right – one out of three people pass the course, so work hard to make that person be you. As it happens, all three of us (myself and both of the people next to me) ended up passing.<\/p>\n
The stats work out as follows. Let’s say we have probability p of contracting the disease and that p<\/span>=1\/N<\/span>. We are shown N people. The probability of no-one contracting the disease is (1-p<\/span>)N<\/sup><\/span>. For the 3 person scenario, that means that there is about a 30% chance that they’re all fine. Of course, that means that there’s a 70% chance that at least one of them will contract the disease, but that’s not quite what they had in mind when they chose to show us three women. If they had chosen N<\/span>=7 (I think that’s for breast-cancer), there would be a 34% chance that everyone was fine.<\/p>\n Even more interesting is that the probability of everyone being fine converges to 1\/e<\/span> (about 37%) as N<\/span> goes to infinity. Perhaps when I figure out a fast way to get nicely rendered equations and plots into this blog I’ll go into more detail.<\/p>\n","protected":false},"excerpt":{"rendered":" I saw an ad on TV yesterday that made me think about statistics. It featured a shot of three women, with voice over saying “1 in three women develop disease X” (can’t remember what it was). The implication, of course, is that one of the three women shown in the picture will develop disease X. […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","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_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[],"tags":[128,173,198],"class_list":["post-70","post","type-post","status-publish","format-standard","hentry","tag-counter-intuitive","tag-musings","tag-statistics"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/posts\/70","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/comments?post=70"}],"version-history":[{"count":0,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/posts\/70\/revisions"}],"wp:attachment":[{"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/media?parent=70"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/categories?post=70"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sandrock.co.za\/carl\/wp-json\/wp\/v2\/tags?post=70"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}