After we hear the second, heads, we cut any branches leading to tails. Therefore, the probability the coin is fair after two heads in a row, is the one fair outcome leading to heads, divided by all possible outcome leading to heads, or one fifth. Notice our confidence in the fair coin is dropping as more heads occur, though realize it will never reach zero. No matter how many flips occur, we can never be 100% certain the coin is unfair. In fact, all conditional probability questions can be solved by growing trees. Let's do one more to be sure. Bob has three coins.