Mary and Jane play a matching pennies game with a fair coin. They simulateously ?ip a penny. If the coins match (both H or both T) Mary wins a penny, and if they do not match, Jane wins a penny. If they play four rounds, what is the probability that Mary ends up with a greater number of pennies than Jane given that Mary wins the ?rst round. Solution M M M J M M J M M J M M these 3 are possibilities that mary ends with high coins so probability = (1/2)^3+(1/2)^3+(1/2)^3 = 3/8 = 0.375.