1. When a tennis player hits his first serve as hard as possible (called a blast), he gets the ball in (that is, within bounds) 60% of the time. When the blast first serve is in, he wins the point 80% of the time. When the first serve is out, his gentler second serve wins the point 45% of the time. Draw a tree diagram representing the probabilities of winning the point for the first two serves. Use the tree diagram to determine the probability that the server eventually wins the point when his first serve is a blast?
2. Suppose that, during any year, the probability of an accidental nuclear war is .0001 (provided, of course, that there hasn't been one in a previous year). Draw a tree diagram representing the possibilities for the next three years. What is the probability that there will be an accidental nuclear war during the next three years?