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Answer :
The expected number of days Pete will catch fish when he goes fishing 3 days next week, given that the probability of catching fish on any given day is 0.88, is 2.64 days.
In this problem, we are interested in the number of days Pete catches fish when he goes fishing three days next week. We define a random variable X to represent the number of days he catches fish. Since each day is an independent trial with a constant probability of success, we can model the number of days Pete catches fish as a binomial distribution.
The binomial distribution is characterized by two parameters: n and p, where n is the number of trials and p is the probability of success in each trial. In this case, we have n = 3 (Pete is going fishing three days) and p = 0.88 (the probability that Pete catches fish on any given day). Therefore, the probability mass function of X is
P(X = k) = (3 choose k) × 0.88^k × (1-0.88)^(3-k)
where k = 0, 1, 2, or 3.
The expected value of a binomial distribution is given by the formula:
E(X) = n × p
Therefore, in this case, the expected number of days Pete catches fish is
E(X) = 3 × 0.88 = 2.64
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