Among the 1,000 policyholders of the auto insurance company, 400 are classified as low-risk drivers and 600 are classified as high-risk drivers. In each month, the probability of zero accidents for high-risk drivers is 0.80 and the probability of zero accidents for low-risk drivers is 0.90. Calculate the expected bonus payment from the insurer to the 1000 policy

Question

Eugene Cross

Business

1 January, 20:07

Among the 1,000 policyholders of the auto insurance company, 400 are classified as low-risk drivers and 600 are classified as high-risk drivers. In each month, the probability of zero accidents for high-risk drivers is 0.80 and the probability of zero accidents for low-risk drivers is 0.90. Calculate the expected bonus payment from the insurer to the 1000 policy

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Emerson Montoya · Answer 1

50,400

Explanation:

We are required to

Calculate the expected bonus payment from the insurer to the 1000 policyholders in one year:

X = case of 0 accident

E[X] = 400 x P (X | low risk) + 600 x P (X | high risk)

= (400 x 0.9) + (600 x 0.8)

= 840

Expected bonus = 840 x 5 dollars x 12 months

= 50400