Suppose you and a friend are betting on a horse race involving four horses. You can win money in one of the following ways:
If horse 3 ?nishes in front of horse 2, you receive $5.
If neither horse 4 nor horse 2 ?nishes last, you receive $5.
Your friend can win money in one of the following ways:
If the winning horse is either horse 1 or horse 3, your friend receives $4.
If horse 1 is second or third, your friend receives $3.
Suppose that the horses are evenly matched, so that all possible finishing orders are equally likely. Let X represent your winnings, and let Y represent your friend's winnings.
(a) Give the joint PMF for X and Y (you may give it in table format).
(b) What is the probability that you win more money than your friend?