When a fisherman catches a fish, it is a young one with a probability of 0.23 and it is returned to the water. On the other hand, an adult fish is kept to be eaten later.
(a) What is the expected number of fish caught by the fisherman before an adult fish is caught?
(b) What is the probability that the fifth fish caught is the first young fish?
Suppose that the fisherman wants three fish to eat for lunch.
(c) What is the probability that the first time the fisherman can stop for lunch is immediately after the sixth fish has been caught'.'
(d) If the fisherman catches eight fish, what is the probability that there are sufficient fish for lunch?