A man and a woman agree to meet at a certain location about 12:30 P. M. If the man arrives at a time uniformly distributed between 12:15 and 12:45, and if the woman independently arrives at a time uniformly distributed between 12:00 and 1 P. M., find the probability that the first to arrive waits no longer than 5 minutes. What is the probability that the man arrives first?
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