Difficulty: Hard

There is a birthday party with a bunch of girls and boys. Someone ate the last piece of cake, but the details are a bit sketchy. Let's assume that statistically, the last piece of cake is eaten by a boy 85 percent of the time. The adult in charge thought that she saw a girl eat the last piece, but we know that the adult is only correct 80 percent of the time. What is the probability that a girl ate the last piece of cake? What is the probability that it was a boy?