Question

A college library has four copies of a certain book; the copies are numbered 1, 2, 3, and 4. Two of these are selected at random. The first selected book is placed on 2- hr reserve, and the second book can be checked out overnight.

a) Suppose that copies 1 and 2 are hardcover books, whereas copies 3 and 4 are softcover books. Let A denote the event that exactly one of the copies selected is a hardcover book.What outcomes are contained in A?

b) What is the probability that exactly one of the books selected is hardcover?

Answer 1

Result:

A college library has four copies of a certain book; the copies are numbered 1, 2, 3, and 4. Two of these are selected at random. The first selected book is placed on 2- hr reserve, and the second book can be checked out overnight.

a) Suppose that copies 1 and 2 are hardcover books, whereas copies 3 and 4 are softcover books. Let A denote the event that exactly one of the copies selected is a hardcover book. What outcomes are contained in A?

A: { (1,3),(1,4), (2,3),(2,4)}

b) What is the probability that exactly one of the books selected is hardcover?

Number of ways Select 2 from 4 books, 4c2 = 6

Number of ways Select exactly one of the books selected is hardcover = 4

The required probability = 4/6 = 0.6667