Final answer:
To calculate the minimum premium, the insurance company should total the expected payments for major and minor accidents based on their probabilities and payouts, resulting in $1,300 as the correct amount.
Step-by-step explanation:
The student is asking how the insurance company should compute the minimum premium for a policy that covers at most one accident, taking into account the probabilities of major and minor accidents and the respective payouts. To calculate this, we need to find the expected payment the insurance would make, which is the sum of the products of the payouts and their respective probabilities.
The expected payment for a major accident is 0.01 (probability) multiplied by $50,000 (payout), and for a minor accident, it is 0.08 (probability) multiplied by $10,000 (payout). Adding these two expected payments gives us the minimum premium the company should charge.
Expected payment for major accident = Probability of major accident x Payout for major accident
Expected payment for major accident = 0.01 x $50,000 = $500
Expected payment for minor accident = Probability of minor accident x Payout for minor accident
Expected payment for minor accident = 0.08 x $10,000 = $800
The minimum premium should therefore be the total of these expected payments: $500 (major) + $800 (minor) = $1,300.
Hence, the correct answer is (b) $1,300.