For the biased coin, we now have two tail leaves and four head leaves, and that is it. When Bob shows the result, Heads! this new evidence allows us to trim all branches, leading to tails, since tails did not occur. So the probability that he chose the biased coin, given heads occur? Well, four leaves can come from the biased coin, divided by all possible leaves. Four divided by ten, or 40%. When in doubt, it's always possible to answer conditional probability questions by Bayes' theorem.