Phil has challenged James to a cribbage contest Noise: Cribbage is a popular card game. The rules of the game are not important for this question. Before the start of the contest, they each put $10 into the pot. They have decided that the rst person to win 10 games wins the pot. It is assumed that they are equally matched so that the probability that either wins any game is 1/2. There are no ties. a. After playing 16 grueling, hard-fought games, they are forced to quit due to fatigue, with James having won '7 games and Phil having won 9 games. They decide to split the pot fairly and go home for the night. At that point, what would James's share of the total pot of $20 be? I). The next day, after a great deal of rest, they decide to play again, setting up a rematch! Now, in order to avoid fatigue, they have decided to play until someone has won 5mm rounds. They each put $10 into the pot again. Well, things do not go according to plan, and they are forced to quit after 9 rounds, with James having won 5 rounds, and Phil having won 4 rounds. They are too tired to continue. once again! Phil tells James that he wants $7.50 from the pot, and he'll go home. Should James take this offer? Justify your