A survey of 12 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) $12 / 86$
B) $43 / 86$
C) $19 / 86$
D) $7 / 86$

Question

A survey of 12 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) $12 / 86$
B) $43 / 86$
C) $19 / 86$
D) $7 / 86$

Quizplus · Accepted Answer

We can use the binomial probability formula to solve this problem:

P(X = k) = (n choose k) * p^k * (1-p)^(n-k)

Where: 
n = 7 (number of people selected) 
k = 4 (number of people who purchased a hardcover book) 
p = 5/12 (probability that one person purchased a hardcover book)

Plugging in the values:

P(X = 4) = (7 choose 4) * (5/12)^4 * (7/12)^3

Simplifying:

P(X = 4) = (35/2) * (625/20736) * (343/1728)

P(X = 4) = 9.23% or 0.0923

Therefore, the probability that four of the seven people selected had purchased a hardcover book is approximately 0.0923 or 19/86.

A Survey of 12 People at a Bookstore Showed That 12/8612 / 8612/86

A Survey of 12 People at a Bookstore Showed That $12 / 86$