1. In a certain species of rats, black dominates over brown. Suppose that a black rat with two black parents has a brown sibling.
(a) What is the probability that this rat is a pure black rat (as opposed to being a hybrid with one black and one brown gene)?
(b) Suppose that when the black rat is mated with a brown rat, all ?ve of their offspring are black. Now, what is the probability that the rat is a pure black rat?
2. There are three coins in a box. One is a two-headed coin, another is a fair coin, and the third is a biased coin that comes up heads 75 percent of the time. When one of the three coins is selected at random and ?ipped, it shows heads. What is the probability that it was the two-headed coin?