Question

One in five people in the United States owns individual stocks. In a random sample of 8 people, what is the probability that exactly 4 of them own a stock?

Answer 1

0.218

Explanation:

The number of ways to choose 4 people out of 8 is 8 choose 4, which can be calculated as C(8,4) = 8! / (4! * (8-4)!). The probability that each chosen person owns a stock is 0.2 and the probability that each not-chosen person doesn't own a stock is 0.8. The desired probability is then:

C(8,4) * (0.2^4) * (0.8^(8-4)) = 70 * 0.0256 * 0.4096 = 0.21807104

So, the probability of exactly 4 people out of 8 owning a stock is approximately 0.218.

Hope this helps!