Philip and Callum play a game of Chinese checkers. Each time they play a game, Philip has a 0.7 chance of winning. Assume the games are independent.
a. In a tournament, Philip and Callum will play 8 games. What is the probability Philip wins exactly 6 games?
b. Philip and Callum decide to keep playing until Callum wins 3 times. What is the probability they play a total of 12 games?
c. How many 8-game tournaments will they expect to have to play until Philip wins exactly 6 games?