Question

According to the Consumer Electronics Manufacturers Association, 10% of all U.S. households have a fax machine and 52% have a personal computer. Suppose 91% of all U.S. households having a fax machine also have a personal computer.

1. What is the probability that a randomly selected U.S. household has a fax machine and a personal computer?

2. What is the probability that a randomly selected U.S. household has a fax machine or a personal computer?

3. What is the probability that a randomly selected U.S. household has a fax machine and does not have a personal computer?

d. Are the events fax machine and personal computer independent? Why?

Answer 1

Let F = fax machine and C = personal computer

Given: P(F) = 0.10, P(C) = 0.52, P(C|F) = 0.91

(a) P(F Ç C) = P(C|F) * P(F) = 0.91 * 0.1 = 0.091

(b) P(F È C) = P(F) + P(C) – P(F Ç C) = 0.10 + 0.52 – 0.091 = 0.529

(c) P(Only F) = P(F) – P(F Ç C) = 0.10 – 0.091 = 0.009

(d) P(C|F) = 0.91 and P(C) = 0.52 are not equal. Therefore the events F and C are not independent.