Question

An automobile insurance company divides customers into three categories: good risks, medium risks, and poor risks. Assume that of a total of 11,124 customers, 7751 are good risks, 2426 are medium risks, and 947 are poor risks. As part of an audit, one customer is chosen at random. Round your answers to four decimal places if necessary.

a) What is the probability that the customer is a good risk?

b) What is the probability that the customer is not a poor risk?

Answer 1

Explanation:

a) The probability that the customer is a good risk is given by the ratio of the number of good risks to the total number of customers. Therefore:

P(customer is a good risk) = 7751/11124 = 0.6968 (rounded to four decimal places)

b) The probability that the customer is not a poor risk is equal to the probability that the customer is a good risk or a medium risk. Therefore:

P(customer is not a poor risk) = P(customer is a good risk or a medium risk)

= P(customer is a good risk) + P(customer is a medium risk)

= (7751 + 2426) / 11124

= 0.9239 (rounded to four decimal places)