Step By Step1of2

Tables Keypad

Keyboard Shortcuts

A large life insurance company is interested in studying the insurance policies held by married couples. In particular, the insurance company is interested in the amount of insurance held by husbands and wives. The insurance company collects data for all of its 1000policies where both the husband and the wife are insured. The results are summarized in the following table.

	Amount of Life Insurance on Husband ($)
0-50,000	50,000-100,000	100,000-150,000	Morethan 150,000
Amount of Life Insurance on Wife ($)	0-50,000	400	200	50	50
50,000-100,000	50	50	30	30
100,000-150,000	20	10	25	25
More than 150,000	20	10	15	15

You were asked to determine the probability that the wife will have between $50,000 and $100,000 of insurance and the husband will have more than $150,000 of insurance for a randomly selected policy.

In the given situation, we are told to randomly select an insurance policy from all of1000policiesthe insurance company has. Therefore, we know the entire sample space and any of the policies from it have the same chance to be selected. These two conditions tell us that we should use the classical approach to find the desired probability. In this approach, the probability of an eventA, denoted P(A)P(A), is given by the following formula.

P(A)=number of outcomes inAtotal number of outcomes in the sample spaceP(A)=number of outcomes inAtotal number of outcomes in the sample space

The eventAconsists of all insurance policies where the wife has between $50,000 and $100,000of insurance and the husband has more than $150,000of insurance. The word "and" tells us that we should count only the policies where both of the two conditions are met. Keeping it in mind, determine the number of outcomes in A.

Answer