Ponderosa Paint and Glass carries three brands of paint. A customer wants to buy another gallon of paint to match paint she purchased at the store previously. She can't recall the brand name and does not wish to return home to find the old can of paint. So she selects two of the three brands of paint at random and buys them. Her husband also goes to the paint store and fails to remember what brand to buy. So he also purchases two of the three brands of paint at random. Determine the probability that both the woman and her husband fail to get the correct brand of paint. (Hint: Are the husband's selections independent of his wife's selections?)
A) 3/2
B) 2/3
C) 1/9
D) 3/4

Question

Quizplus · Accepted Answer

The probability that the woman fails to get the correct brand is 2/3, and the probability that the husband also fails is 2/3. Since their selections are independent, the combined probability is (2/3) * (2/3) = 4/9. However, the question asks for the probability that both fail to get the correct brand, which is 1 - 4/9 = 5/9. But since the question asks for the probability that both fail, the correct calculation is (1/3) * (1/3) = 1/9.

Ponderosa Paint and Glass Carries Three Brands of Paint