Example 10 Riley is a rising star in the school tennis club. He has found that when he gets his first serve in the probability that he wins that point is 0.75. When he uses his second serve (because he does not get his first serve in) there is a 0.45 chance of him winning the point. He is successful at getting his first serve in on three out of five occasions and the second serve in on three out of four occasions. a Find the probability that the next time Riley serves he wins the point. b Given that Riley wins the point, what is the probability that he got his first serve in