This is a binomial probability problem where you are trying to find the probability of a certain number of "successes" (in this case, visitors arriving at the website in error) in a certain number of trials (in this case, 8 visitors).

The formula for binomial probability is:

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

where:
- P(X=k) is the probability of k successes,
- C(n, k) is the combination of n items taken k at a time,
- p is the probability of success on a single trial, and
- n is the number of trials.

In this case, p = 0.15 (the probability a visitor arrives at the website in error), n = 8 (the number of visitors), and we want to find the probability that fewer than 3 of them arrive in error, i.e., P(X

Question

This is a binomial probability problem where you are trying to find the probability of a certain number of "successes" (in this case, visitors arriving at the website in error) in a certain number of trials (in this case, 8 visitors).

The formula for binomial probability is:

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

where:
- P(X=k) is the probability of k successes,
- C(n, k) is the combination of n items taken k at a time,
- p is the probability of success on a single trial, and
- n is the number of trials.

In this case, p = 0.15 (the probability a visitor arrives at the website in error), n = 8 (the number of visitors), and we want to find the probability that fewer than 3 of them arrive in error, i.e., P(X<3).

P(X<3) = P(X=0) + P(X=1) + P(X=2)

We can calculate each of these probabilities using the binomial probability formula:

P(X=0) = C(8, 0) * (0.15^0) * ((1-0.15)^(8-0)) = 0.279
P(X=1) = C(8, 1) * (0.15^1) * ((1-0.15)^(8-1)) = 0.377
P(X=2) = C(8, 2) * (0.15^2) * ((1-0.15)^(8-2)) = 0.282

Adding these probabilities together gives:

P(X<3) = 0.279 + 0.377 + 0.282 = 0.938

So, the probability that fewer than 3 of the 8 visitors arrive at the website in error is approximately 0.938, or 93.8%.

Knowee AI · Accepted Answer