Philip and Callum are playing Monopoly. Callum has an 80% chance of winning whenever he plays Philip. If they play Monopoly until somebody wins 3 games (assuming no ties and that the games are independent):
a. What is the probability that Callum wins the series in exactly 3 games? In 4 games? In 5 games?
b. What is the probability Philip wins the series in exactly 3 games? In 4 games? In 5 games?
c. Given that the series took 5 games, what is the probability that Callum won?
d. Given that Callum wins the series, what is the expected number of games that the boys play?