Assuming a binomial distribution, four percent of the customers of a mortgage company default on their payments. A sample of five customers is selected. What is the probability that at most two customers in the sample will default on their payments?

We will use binomial distribution in this problem.

The solution would be like this for this specific problem:

P (default) = p = 4% = 0.04

q = 1-p = 1-0.04 = 0.96

n = 5

P (r) = nCr*q^ (n-r) * p^r

Required probability = P (r=2) = 5C2*0.96^3*0.04^2

= 0.0142 OR 1.42%

The probability that at most two customers in the sample will default on their payments is 1.42%.