Suppose that a person wins a game of chance with probability 0.40, and loses otherwise. He plays the game until he wins for the first time, and then he stops. Assume that the games are independent of each other. Let X denote the number of games that he must play until (and including) his first win.
a. How many games does he expect to play until (and including) his first win?
b. What is the variance of the number of games he plays until (and including) his first win?
c. What is the probability that he plays 4 or more games altogether?