I toss two coins and look at the outcome. I then tell you that at least one of the coins is showing up as "tails". What is the chance that the other one is showing "tails" as well?

(from techInterview.org)

Yes, the results of independant events (including previous instances of the same tossing of the coin) do not affect the probability. But this is not an independant event. If Art tossed a nickel and a dime and then announced that the dime was "tails," that would be an independant event. If he announced that one of the coins was tails (or any other non-informative statement)and asked you to predict whether the nickel was heads or tails, that would be an independant event. But he only said that one of them came up "tails." There are three possibilities: The dime is "tails" and the nickel is "heads"; the dime is "heads" and the nickel is "tails"; or they are both "tails". So there is a 1 in 3 chance that they are both tails.

Posted by TomM on 2002-05-10 23:11:08