Joe and Pete each have two cents in their pockets. They have decided to match pennies; that is, they will each take one of their own pennies and flip them. If the pennies match (two heads or two tails), Joe gets Pete’s penny; if the pennies do not match, Pete gets Joe’s penny. They will keep repeating the game until one of them has four cents, and the other one is broke. Although they do not realize it, all four pennies are biased. The probability of tossing a head is 0.6, and the probability of a tail is 0.4. Let X be a Markov chain where Xn denotes the amount that Joe has after the n-th play of the gam a) Give the Markov matrix for X b) What is the probability that Joe will have four pennies after the second toss?

c) What is the probabilty that Pete will be broke after 3 tosses?

d) What is the probability that the game will be over after the third toss?

e) What is the expected amount of money Pete will have after two tosses?