In professional tennis, the server often tries to ace her opponent on the first serve. If the first serve is out of bounds, the server tries to be more accurate with the second and last serve. From records of women's tennis at Wimbledon3 the probability is .61 that the first serve is in bounds. When the first serve is in, the server wins the point with probability .62. When a second serve is required, the probability is .86 that it is in bounds but the probability drops to .54 of ultimately winning the point. For a typical player, with these probabilities, determine
(a) The probability of winning the point when serving.
(b) If you only know that she wins the point, what is the probability she won on the first serve?