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 expected number of days Pete will catch fish is
A) 0.56.
B) 0.88.
C) 2.64.
D) 0.3168.

Question

Quizplus · Accepted Answer

The probability of catching fish on any given day is 0.88. Let X be the random variable defined as the number of days Pete catches fish over the three-day period. X can take on the values of 0, 1, 2, or 3. The expected value of X can be calculated as:

E(X) = Σ(xP(x))

Where Σ is the sum over all possible values of X, x is the value of X, and P(x) is the probability of X taking on the value x.

For this problem:

E(X) = 0(0.12)^3 + 1(0.88)(0.12)^2 + 2(0.88)^2(0.12) + 3(0.88)^3
E(X) = 0 + 0.1056 + 0.370944 + 0.515584
E(X) = 2.64

Therefore, the expected number of days Pete will catch fish is 2.64, which is choice C.

The Probability That Pete Will Catch Fish When He Goes