You consider the probability that a coin is double-headed to be 0.01 (call this option

????????); if it isn’t double-headed, then it’s a fair coin (call this option ????). For whatever reason, you can only test the coin by flipping it and examining the coin (i.e., you can’t simply examine both sides of the coin). In the worst case, how many tosses do you need before having a posterior probability for either ???? or ???????? that is greater than 0.99, i.e., what’s the maximum number of tosses until that happens?