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Old 04-04-2003, 09:54 AM
BruceZ BruceZ is offline
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Join Date: Sep 2002
Posts: 1,636
Default Re: creating a 2:1 shot with a fair coin

Say I tell you one of the coins is heads. Now the only possible outcomes were HH,HT,TH, so the probability that the other one is heads is 1/3. This is the same as the classic problem where I tell you I have two children and one is a boy; the probability that the other one is a boy then becomes 1/3.

The reason I have to choose randomly is because if I always told you say "heads" when it was HT or TH, and you pick up on this, then whenever I tell you "tails" you would know it was TT. Or if one of the coins had some distinguishing feature, and I always chose that coin to tell you about, and you knew this, then the probability becomes 1/2 since when I say "heads", now the only outcomes are HH,HT, since you would know one particular coin was heads.
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