Question

Please answer the following with all steps

9. When a fisherman catches a fish, it is a young one with probability 0.235 and it is returned to the water. On the other hand, an adult fish is kept to be eaten later. a. What is the probability that the fifth fish caught is the first young one? b. Suppose that the fisherman wants three fish to eat for lunch. What is the probability that the fisherman can stop for lunch immediately after the sixth fish has been caught? Suppose that the fisherman wants three fish to eat for lunch. If the fisherman catches 8 fish, what is the probability that there are sufficient fish for lunch?

Answer 1

a)Probability =P(getting four adult fish and then 1 younger fish) =(1-0.235)⁴*0.235=0.0805

b)Probability =P(getting 2 adult fish till 5th fish and getting 3rd adult fish on 6th try) =$\binom{5}{2}(0.765)^{3}(0.235)^{3}$

=0.0581

c)

Probability =P(at least 3 adult fish in 8) =1-P(at most 2 adult fish) =1-$\sum_{x=0}^{2}\binom{8}{x}(0.765)^{x}(0.235)^{8-x}$

=1-0.0030 =0.9970