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#2
04-04-2003, 03:02 AM
 BruceZ Senior Member Join Date: Sep 2002 Posts: 1,636
Re: creating a 2:1 shot with a fair coin

It can be done with conditional probabilities. Flip two coins at the same time. It is important that you cannot tell the coins apart. The possible outcomes are HH,TT,HT,TH. Show your friend one of the coins. You have to select the coin to show at random to be fair. The probability that the other coin is the same will be 1/3. Notice that if the coins can be distinguished, the probability will be 1/2. An alternative to having indistinguishable coins is to tell your friend the value of one of the coins, but don't show him either coin until after he guesses. A way you can select one of the coins at random to show is to flip a 3rd coin. If it comes up heads, show or tell him about the coin that is a head, if it comes up tails, show or tell him about the coin that is a tail. If both coins were the same, it doesn't matter which one you show or tell him about.