Suppose Tom and Jim are bored at home when Jim proposes the following game: The two of them will take out all of the pennies in their pockets to serve as their starting bankrolls (Tom had 13 pennies, Jim had 27). They will then flip a coin. If the coin lands on heads, Tom wins and Jim gives him a penny. If the coin lands on tails, Jim wins and Tom gives him a penny. Whoever gets all of the pennies wins the game.

(1) What is the probability that Tom wins all of the pennies?

(2) What is the probability that Jim wins all of the pennies?

(3) What is the probability that the game will not terminate? Why?

(4) What is the expected number of coin flips until Tom and Jim's game ends?