Question

Joe's, a Chicago-style pizzeria chain, states that 50% of its customers order for delivery. If this percentage is correct, what is the probability that, in a random sample of 4 Joe's customers, exactly 2 order for delivery?

A. 25%
B. 37.5%
C. 50%
D. 62.5%

Answer 1

The probability that exactly 2 out of 4 customers order for delivery is 37.5%, which is option B.

Step-by-step explanation:

To solve the question of what the probability is that, in a random sample of 4 Joe's customers, exactly 2 order for delivery, 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 (in this case, 4 customers).
• k is the number of successes (2 customers ordering for delivery).
• p is the probability of a single success (0.50 for delivery according to Joe's).

Substituting these values into the formula, we get:

P(X = 2) = (4 choose 2) * 0.50^2 * (1 - 0.50)^(4 - 2)

Calculating this gives:

P(X = 2) = 6 * 0.25 * 0.25 = 0.375

So the probability is 0.375, or 37.5%, making option B the correct answer.