Suppose a man has ordered twelve 1-gallon paint cans of a particular color (lilac) from the local paint store in order to paint his mother's house. Unknown to the man, three of these cans contains an incorrect mix of paint. For this weekend's big project, the man randomly selects four of these 1-gallon cans to paint his mother's living room. Let $x =$ the number of the paint cans selected that are defective. Unknown to the man, $x$ follows a hypergeometric distribution. Find the mean of this distribution.
A) 4
B) 12
C) 1
D) 3

Question

Quizplus · Accepted Answer

The mean of a hypergeometric distribution is given by $ \frac{n \cdot K}{N} $, where $ n $ is the number of draws (4), $ K $ is the number of successes in the population (3 defective cans), and $ N $ is the population size (12 cans). Thus, the mean is $ \frac{4 \cdot 3}{12} = 1 $.

Suppose a Man Has Ordered Twelve 1-Gallon Paint Cans of a Particular