Consider a simple card game where there are four cards labeled 1, 2, 3, and 4. Each round, my friend first draws a card randomly from the four. After my friend draws the card, I also randomly draw a card. Each round, my friend and I each put in $1 into the pool. The person with the higher card takes the money in the pool. The cards are then reshuffled for the next round.

a) What is the probability that I would win each round?

b) What is the probability I will win two of the next four rounds?

c) What is the probability that after 4 rounds I have the same amount of money as when I started?

d) If I start off with only $1 and once I run out of money, I will stop playing the game.

What is the probability that I play at least 4 rounds?