Question

A book shelf holds twenty books. Eleven are hard-covered, nine of the books are nonfiction, and four of the nonfiction books are hard-covered, as shown in the Venn diagram. Let event H be a hard-covered book and let event N be a nonfiction book.

Circles H and N intersect. Circle H contains 7, circle N contains 5, and the intersection contains 4. Number 4 is outside of the circles.

A book is chosen randomly. Complete the steps to find the probability that the book is nonfiction given that it is hard-covered.

Find the probability that a chosen book is nonfiction and hard-covered. P(N ∩ H) =
Find the probability that a chosen book is hard-covered. P(H) =
Calculate the conditional probability.
StartFraction P (N intersection H) Over P (H) EndFraction =

Answer 1

P(N ∩ H) = 4/20 = 1/5

P(H) = 11/20

P(N | H) = (4/20) / (11/20) = 4/11