Two players (player A and player B) are playing a game against each other repeatedly until one is bankrupt. When a player wins a game they take $1 from the other player. All plays of the game are independent and identical.

a) (5 marks) Suppose player A starts with $6 and player B starts with $6. If player A wins a game with a probability of 0.50, what is the probability the game ends (someone loses all their money) on exactly the 10th play of the game?

b) (5 marks) Suppose player A starts with $2 and player B starts with $3. If player A wins a game with probability p, what is the probability that player A wins all the money?

Answer rating: 100% (QA)

a To find the probability that the game ends on exactly the 10th play we need to consider the possible sequences of wins and losses for both players t... View the full answer