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

Quizplus · Accepted Answer

We need to use the binomial distribution formula to solve this problem. Let's first calculate the probability of one person having purchased a hardcover book:
P(purchased hardcover book) = 5/12
P(did not purchase hardcover book) = 7/12

Using the binomial distribution formula, we get:
P(4 out of 7 selected purchased hardcover book) = (7 choose 4) * (5/12)^4 * (7/12)^3
= 35 * 0.042875232 * 0.1852208
= 0.353615608

Therefore, the probability of four out of seven selected individuals having purchased a hardcover book is 0.353615608 or approximately 19/86. The best choice is C. First find the probability of selecting four people who had purchased hardcover books and three who had not:
(5/12) x (4/11) x (3/10) x (2/9) x (7/8) x (6/7) x (5/6) = 1/132
Then, since there are (7 choose 4) = 35 ways to choose four people out of seven, multiply this probability by 35:
35 x 1/132 = 35/462 = 5/66
Simplify this fraction to get the final answer of 19/86. Therefore, the best choice is C.

A Survey of 12 People at a Bookstore Showed That