(a) A fisherman casts his fishing rod into a lake where on each cast he catches a fish with probability 0.02. What is the probability he will require more than 40 casts to catch his first fish? Provide a numeric answer.

(b) The fisherman will go home if he catches 5 fish. What is the expected number of casts he will require to catch 5 fish?

(c) The fisherman makes 100 casts. What is the probability he catches 2 fish? Provide a numeric answer.