Question

There are three insurance companies in the Business District in Accra. It is known from previous records that each year, 2 percent, 5 percent, and 3 percent of those insured by Vanguard Insurance, Enterprise Insurance, and Star Insurance respectively submit claims. 20 percent of the people in the community have an insurance policy with Vanguard Insurance Company, 30 percent with Enterprise Insurance Company, and 50 percent with Star Insurance Company.

(i) What is the probability that a randomly selected insurance policyholder in the community made a claim in a certain year?
A) 3.5 percent
B) 4 percent
C) 4.5 percent
D) 5 percent

Answer 1

To find the probability that a randomly selected policyholder made a claim, we calculate the weighted probabilities for each insurance company and sum them up. The final probability is 3.4%, so the closest answer is 3.5% (Option A).

Step-by-step explanation:

The question asks for the probability that a randomly selected insurance policyholder in the community made a claim in a certain year. This probability is determined by considering the percentage of policyholders with each insurance company, as well as the percentage of claimants for each company. To solve this, we can use the law of total probability which considers each source of policies and their respective claim rates.

First, we calculate the weighted probability of submitting a claim for each insurance company:

• Vanguard Insurance: 20% policyholders × 2% claims = 0.2 × 0.02 = 0.004 or 0.4%
• Enterprise Insurance: 30% policyholders × 5% claims = 0.3 × 0.05 = 0.015 or 1.5%
• Star Insurance: 50% policyholders × 3% claims = 0.5 × 0.03 = 0.015 or 1.5%

Adding these probabilities gives us the overall probability that a randomly selected policyholder made a claim:

0.004 + 0.015 + 0.015 = 0.034 or 3.4%

The closest answer to 3.4% is Option A) 3.5 percent, which is the probability that a randomly selected insurance policyholder in the community made a claim in a certain year.