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 problem follows a binomial distribution with n=400 (number of policies) and p=0.0005 (probability of a claim). The formula for the probability of exactly k successes in n trials is:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

Substituting n=400, p=0.0005, and k=2, we get:

P(2) = (400 choose 2) * (0.0005)^2 * (1-0.0005)^(400-2)
P(2) = (400*399/2) * 0.00000025 * 0.818309
P(2) = 0.061382

Therefore, the probability that exactly two claims will be filed is 0.0614, which corresponds to choice C.

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