This is actually a problem from some biological data, but can be more generally described as follows: I have a bag containing n coins. Each coin has a heads and a tails. After the coin has been flipped some number of times, it vanishes. The number of times the coin may be flipped varies from coin to coin. I flip all the coins in the bag until they've each vanished, and carefully record each outcome. I know that the bag is either filled with fair coins, or is filled with coins that have a bias toward heads or tails. Each of the coins may have a different bias. My question is this: if it is the latter case, how might I reject the possibility that it is in fact a bag of fair coins?