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12 March, 11:40

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?

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  1. 12 March, 11:47
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    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%.
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