Lost Town and Finder's Town: Bayesian ProbabilityDate: 04/27/99 at 16:08:18 From: Wally Ming Subject: Probabilities A man is lost in the mountains. There is a town located near him called Lost Town that's populated with 10 males and 10 females. Another town that's also close is Finder's Town with a population of 4 females and 16 males. He has no idea what town he's in, but he spots a male. What is the probability that he wandered into Finder's town? What is the probability he wandered into Lost Town? They way I tried to solve it: There's a 50% (10/20) chance that he meets up with a male if he wanders into Lost Town. There's a 80% (16/20) chance he meets a male if he wanders into Finder's town. .50(10) = 5% chance the guy is in Lost Town .80(16) = 12.8% chance the guy is in Finder's Town Is this right? Date: 04/27/99 at 18:51:13 From: Doctor Anthony Subject: Re: Probabilities This is an example of Bayesian probability. You are given extra information that changes the probabilities from those you expect before the experiment begins. In this case the extra information is that he spots a male Lost Town Finder's Town Prob = 1/2 Prob = 1/2 ------------------------------------- (1/2)(1/2) (1/2)(16/20) He spots a male = 1/4 = 2/5 The sample space is confined to the sum of these two probabilities since he spots a male. 1/4 1/4 The probability he is in Lost Town = --------- = ------- 1/4 + 2/5 13/20 = 5/13 and the probability he is in Finder's Town is then 8/13. Note that the two probabilities MUST sum to 1 since he is certainly in one or the other of the towns. - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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