A large lake is stocked with 30% catfish. You go out on the lake to fish, and each fish you catch that is not a catfish is thrown back into the lake. (Assume that each time you catch a fish, it is independent of the other fish you have caught.) Let X be the number of tries it takes until you catch your first catfish.
(a) What is the average (expected) value for X?
(b) What is the probability that X is at most 3?
(c) What is the probability that X is more than 7?
(c) Suppose that the first 7 fish you caught were not catfish. What is the probability that the next 7fish will also not be catfish?
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