A swimmer is competing in two events at a swim meet. From past experience, he knows that his times in the 100-meter freestyle event follow a normal distribution with mean 52.9 seconds and standard deviation 0.65 seconds. His times in the 100-meter butterfly follow a normal distribution with mean 55.5 seconds and standard deviation 0.9 seconds. He also knows that his times for the two races are independent.
a) What is the probability that he has a faster (lower) time in the freestyle than in the butterfly?
b) What is the probability that his time is the same for both races?