Here's a related problem that helps to understand the coin problem: I have two children. The youngest is a boy. What is the probability both are boys? The answer is 1/2. Now compare to this: I have two children. One of them is a boy. What is the probability that both are boys? It is not 1/2, as it is not specified which child is a boy in the initial information. To solve this, we consider all possibilities for two children: BB, BG, BG and GG. Since we are told one child is a boy, we eliminate GG as a possibility. There are then 3 equally likely possibilities: BB, BG and GB. The chance that both are boys are 1/3, and the chance that one is a boy and one is girl is 2/3. With the coin problem, each head flipped adds some information and the probability changes in an equally weird kind of way...