what is the probability that, in a random sample of 6 visitors to the website, exactly 2 arrive in error?

Question

A certain company's IT department has found that 17% of all visitors to the company website arrive there in error. (They are actually looking for another website.) If this percentage is correct, what is the probability that, in a random sample of 6 visitors to the website, exactly 2 arrive in error?

Answer 1

You're given the probability of an event, P(arrive in error) = 0.17, and the outcome is dichotomous (no error, error). This is a binomial distribution problem.

n = 6

x = 2

n - x = 6 - 2 = 4

p = 0.17

q = 1 - p = 1 - 0.17 = 0.83

P_x = (_nC_x)p^xq^(n-x) = (6!/[(6-2)!(2!)])*(0.17)²(0.83)⁴ = 0.2057

The probability that, out of 6 visitors, 2 visitors arrived in error is 0.2057.