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. (If necessary, consult a list of formulas.)

This is a binomial probability problem. The binomial probability formula is:

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

where:

• P(X=k) is the probability of k successes in n trials
• C(n, k) is the combination of n items taken k at a time
• p is the probability of success on a single trial
• n is the number of trials
• k is the number of successes

In this case:

• n = 5 (the number of visitors)
• k = 4 (the number of visitors we're interested in)
• p = 0.05 (the probability that a visitor is looking for the website)

First, calculate C(n, k), which is the number of combinations of n items taken k at a time. This can be calculated as:

C(n, k) = n! / [k!(n-k)!]

where "!" denotes factorial. So:

C(5, 4) = 5! / [4!(5-4)!] = 5

Next, calculate p^k and (1-p)^(n-k):

p^k = (0.05)^4 = 0.00000625 (1-p)^(n-k) = (0.95)^1 = 0.95

Finally, substitute these values into the binomial probability formula:

P(X=4) = C(5, 4) * (0.05^4) * (0.95^1) = 5 * 0.00000625 * 0.95 = 0.0000296875

So, the probability that exactly 4 out of 5 randomly selected visitors are looking for the website is approximately 0.00003 when rounded to five decimal places.

This is a binomial probability problem. The binomial probability formula is:

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

where:

• P(X=k) is the probability of k successes in n trials
• C(n, k) is the combination of n items taken k at a time
• p is the probability of success on a single trial
• n is the number of trials
• k is the number of successes

In this case:

• n = 5 (the number of visitors)
• k = 4 (the number of visitors we're interested in)
• p = 0.05 (the probability that a visitor is looking for the website)

Substituting these values into the formula gives:

P(X=4) = C(5, 4) * (0.05^4) * ((1-0.05)^(5-4))

Calculating the combination C(5, 4) gives 5.

So:

P(X=4) = 5 * (0.05^4) * ((1-0.05)^(5-4))

Calculating this gives:

P(X=4) = 5 * 0.00000625 * 0.95

P(X=4) = 0.0000296875

Rounding to three decimal places gives P(X=4) = 0.000.

So, the probability that exactly 4 out of 5 randomly selected visitors are looking for the website is 0.000.