Question

A and B play a coin-flipping game with a fair coin. After each flip, the loser transfers one penny to the winner. The game ends when one player has all the pennies. If at the beginning A and B has m and n pennies respectively, what is the winning probability of A? What's the expected number of coin flips before the game ends?

Answer 1

a)since probability of winning is equal for both players p=1/2

winning probability of A =number of coins with A/total number of coins =m/(m+n)

b)

expected number of coin flips before the game ends =N(pennies with plater A)*N(pennies with player B)=m*n