Joe and Pete each have two cents in their pockets. They have decided to match
pennies; they will each take one of their 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 has four cents, and the other is broke. Although
they do not realize it, all four pennies are biased. The probability of tossing a head is 0.3,
and the probability of a tail is 0.7. Let X be a Markov chain where Xn denotes the amount
that Joe has after the nth play of the game.

(a) Give the one-step Markov matrix for Xn.
(b) What is the probability that Pete will have four pennies after the second toss?
(c) What is the probability that the game does not end after 10 tosses?

Answer rating: 100% (QA)

Ans a b states number of Joes pennies 01 4 in below 2 x 06 06 06 04 04 ma... View the full answer