Question

The probability that Pete will catch fish when he goes fishing is 0.8. Pete is going to fish 5 days next week. Define the random variable x to be the number of days Pete catches fish. What is the probability that Pete will catch fish on exactly two days? Round your answer to the nearest thousandth (3 decimal places).​

Answer 1

Consider x, since there is a fixed number of days Pete goes fishing (equal to 5), on each day he has two outcomes (catching fish or not catching fish) and on each day he catches fish with probability 0.8 independent of other days, thus we can conclude that:

x ~ Binomial(n = 5, p = 0.8) and the probability mass function of x is given by:

Thus, the probability that Pete will catch fish on exactly 2 days is given by:

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