Calculating a Premium for Multiple Risk Scenarios
An insurance provider is designing a one-year policy for a professional photography equipment bag valued at $10,000. Based on data from similar policies, the insurer identifies three distinct, mutually exclusive risk scenarios for any given policyholder:
- A 1% probability of total loss (e.g., theft), resulting in a claim for the full value.
- A 3% probability of major damage, resulting in an average repair claim of $4,000.
- A 5% probability of minor damage, resulting in an average repair claim of $500.
To ensure the policy is financially viable, the insurer needs to set a premium that, at a minimum, covers the total expected claim amount from all potential risks. Analyze the provided data to determine this minimum premium. Show your calculations and explain your reasoning.
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An insurance company offers two separate one-year policies for full coverage against total loss.
- Policy A is for a piece of equipment valued at $5,000 with a 4% probability of loss. The premium for Policy A is $240.
- Policy B is for an art piece valued at $20,000 with a 1% probability of loss. The premium for Policy B is $230.
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