Question

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?

Answer 1

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%.