Statistics?

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?

Answer 1

Assume you want exactly 4 of 7. If 5/12=p is the probability that one person will buy a book, then 7/12=q is the probability that one person will not buy a book. With a sample size of 7 people, the binominal distribution (p(buy)+q(no buy))^7 will apply. This has 8 terms, and the left-most is that all 7 buy the book. The 4th term is that 4 buy the book. This term is 7!/4!3! [ p^4q^3]