Question

In a metropolitan area, 9 out of 10 households have a VCR. Let X denote the number among four randomly selected households that have a VCR. The probability P(X=2) is:

a. 0.145
b. 0.324
c. 0.656
d. 0.129

Answer 1

The probability P(X=2) can be calculated using the binomial probability formula.

Step-by-step explanation:

The random variable in this question is X, which represents the number of households among four randomly selected households that have a VCR. The probability P(X=2) can be calculated using the binomial probability formula:

P(X=k) = C(n,k) * p^k * (1-p)^(n-k)

Here, n = 4 (number of trials), k = 2 (number of success), and p = 0.9 (probability of success). Plugging in these values, we get:

P(X=2) = C(4,2) * 0.9^2 * (1-0.9)^(4-2) = 6 * 0.9^2 * 0.1^2 = 0.145

Therefore, the probability P(X=2) is 0.145 (option a).