A jar contains 100 marbles. Suppose that 30 of the marbles are RED. Marbles will be drawn from the jar as described below. Let X be the number of drawings WITH replacement until you remove your FIRST red marble. Let Y be the number of drawings WITH replacement until you remove your THIRD red marble. Let Z be the number of red marbles removed if you draw 12 marbles WITHOUT replacement.

(a) Calculate E[X].

(b) Calculate P(Y = 12).

(c) Calculate Var(Z).