I’ve filed this in science as it’s basically a mathematical conundrum. I was chatting about this subtle problem with R last night. She’s a self-confessed numbers phobic but interested in how the world works. I worship at the altar of Phi and am perfectly willing to believe a logical mathematical prediction even if it flies in the face of a more immediate intuition. The Monty Hall problem is called after the presenter of a 60s\/70s game show called “Let’s Make a Deal”. It’s a weaker version of the 3 prisoners problem and is generally stated as<\/p>\n
Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what’s behind the doors, opens another door, say No. 3, which has a goat. He then says to you, “Do you want to pick door No. 2?” Is it to your advantage to switch your choice?<\/em><\/p><\/blockquote>\n
We’re also asked to assume that the host is honest, the show isn’t rigged, we have no prior knowledge of the appearance of the goat and a whole bunch of other “butterfly wings”<\/em> that could influence the result in any way. The answer is that it IS to your advantage to switch doors. For example if you pick door A and the host shows you a goat behind door C your first pick was made with a probability of 1 in 3 of correctly identifying the one door with the car behind it from 3 equally advantageous probabilities. The mistake that most people (almost everyone) seems to make is that they then misunderstand the probabilistic basis for switching. I also don’t particularly like the Goat-1,Goat-2 explanation presented by some including professional smart person Marilyn Vos Savant<\/a>.
\nWhen A was picked I had a 1\/3 chance of finding a car but I had a 2\/3 chance of finding a goat. I suppose it depends on how you feel about goats but I’m indifferent and would prefer a car. The resale value is generally higher, unless it’s an Alfa of course! Changing to door B doesn’t have a 2\/3 chance of finding a goat. There’s only one goat left. Damn, I’ve halved my chances of finding a goat. So let’s let the probability that switching to door B is a good by P(SwitchB).
\nP(SwitchB) = P(A was a goat) = 1 - (1\/3) = 2\/3<\/code>
\nThe probability that switching is a good idea is DIRECTLY affected by the probability the first choice was a goat. You can’t ignore the past and must treat the problem as a continuation of the same game. This in itself makes sense but for several reasons our brains find it difficult to combine temporal and logical context and we get a bit confused.<\/p>\n","protected":false},"excerpt":{"rendered":"I’ve filed this in science as it’s basically a mathematical conundrum. I was chatting about this subtle problem with R last night. She’s a self-confessed numbers phobic but interested in how the world works. I worship at the altar of Phi and am perfectly willing to believe a logical mathematical prediction even if it flies […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1701],"tags":[83,84],"_links":{"self":[{"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=\/wp\/v2\/posts\/208"}],"collection":[{"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=208"}],"version-history":[{"count":4,"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=\/wp\/v2\/posts\/208\/revisions"}],"predecessor-version":[{"id":671,"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=\/wp\/v2\/posts\/208\/revisions\/671"}],"wp:attachment":[{"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaisan.com\/blogs\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}