Sweetwater & Associates write weekend trip insurance at a very nominal charge. Records show that the probability that a motorist will have an accident during the weekend and file a claim is 0.0005. Suppose they wrote 400 policies for the coming weekend, what is the probability that exactly two claims will be filed?

Question

Quizplus · Accepted Answer

This is a binomial distribution problem with n=400, p=0.0005, and we want to find the probability of exactly two successes (claims). 
Using the formula for binomial distribution, P(X=2) = (n choose 2) * p^2 * (1-p)^(n-2)
= (400 choose 2) * (0.0005)^2 * (0.9995)^398 
= 0.0164 
Therefore, the probability that exactly two claims will be filed is 0.0164.

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