Answer to Question #252768 in Statistics and Probability for meg28

Question

Not all visitors to a certain company's website are customers. In fact, the website administrator estimates that about 12% of all visitors to the website are looking for other websites. Assuming that this estimate is correct, find the probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website.

Answer 1

Let X denote the number of visitors that are actually looking for the website.

X ~ Bin (n=4, p=0.88)

$P(X=x) = \binom{4}{x}(0.88)^x(1-0.88)^{4-x} \\ P(X=2) = \binom{4}{2}(0.88)^2 (1-0.88)^{4-2} = 0.0669$