Question

Not all visitors to a certain company's website are customers. In fact, the website administrator estimates that about 5% 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 5 visitors to the website, exactly 4 actually are looking for the website. Round your response to at least three decimal places

Answer 1

To find the probability that, in a random sample of 5 visitors to the website, exactly 4 are actually looking for the website, we can use the binomial probability formula.

Step-by-step explanation:

To find the probability that, in a random sample of 5 visitors to the website, exactly 4 are actually looking for the website, we can use the binomial probability formula.

The binomial probability formula is:

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

Where:

P(X=k) is the probability of getting exactly k successes,

n is the number of trials,

p is the probability of success in a single trial,

q is the probability of failure in a single trial,

C(n, k) is the number of combinations of n items taken k at a time.

In this case, n = 5, k = 4, p = 0.05, and q = 0.95.

Plugging these values into the formula:

P(X=4) = C(5, 4) * (0.05)^4 * (0.95)^(5-4)

Simplifying:

P(X=4) = 5 * (0.0025) * (0.95)

P(X=4) = 0.011875

Therefore, the probability that in a random sample of 5 visitors to the website, exactly 4 are actually looking for the website is approximately 0.011875.