An insurance company is issuing 16 car insurance policies. Suppose the probability for a claim during a year is 15 percent. If the binomial probability distribution is applicable, then the probability that there will be at least two claims during the year is equal to:

Question

Quizplus · Accepted Answer

The problem asks for the probability of at least two claims, which means we need to calculate the probability of two claims or more.

Let X be the number of claims during a year. We know that X follows a binomial distribution with n = 16 (number of policies) and p = 0.15 (probability of a claim).

We can use the binomial probability formula to calculate the probability of two or more claims:

P(X ≥ 2) = 1 - P(X < 2) = 1 - P(X = 0) - P(X = 1)

P(X = 0) = (0.85)^16 = 0.117
P(X = 1) = 16C1(0.15)(0.85)^15 = 0.304

Therefore,

P(X ≥ 2) = 1 - 0.117 - 0.304 = 0.579

The closest answer choice is C (0.7161), but that is not correct. The correct answer is actually 0.579, which is closest to answer choice B (0.2775).

An Insurance Company Is Issuing 16 Car Insurance Policies