The probability that Pete will catch fish when he goes fishing is .88. Pete is going to fish 3 days next week. Define the random variable x to be the number of days Pete catches fish. The probability that Pete will catch fish on exactly one day is
A) 0.880.
B) 0.038.
C) 0.040.
D) 0.960.

Question

Quizplus · Accepted Answer

We can use the binomial probability formula:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials, k is the number of successes, p is the probability of success on each trial, and (n choose k) is the binomial coefficient.

In this case, n=3, p=0.88, and we want to find P(X=1). So we plug in those values:
P(X=1) = (3 choose 1) * 0.88^1 * 0.12^2
= 3 * 0.88 * 0.0144
= 0.038016

So the answer is B, 0.038.

The Probability That Pete Will Catch Fish When He Goes