A survey of 11 people at a bookstore showed that five had purchased a hardcover book. If seven people are selected at random, what is the probability that four of them had purchased a hardcover book?
A) 0.076
B) 0.250
C) 0.303
D) 0.606

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 = sample size = 7
k = number of people who purchased hardcover book = 4
p = probability of purchasing a hardcover book = 5/11

Plugging in values, we get:

P(X = 4) = (7 choose 4) * (5/11)^4 * (6/11)^3

P(X = 4) = (35) * (0.041) * (0.271)

P(X = 4) = 0.303

Therefore, the probability that four of the seven selected people had purchased a hardcover book is 0.303. The answer is choice C.

A Survey of 11 People at a Bookstore Showed That