To answer these questions, we’ll calculate the expected cost to the insurance company based on the probabilities and potential loss. This approach will give us the average amount they expect to lose and help determine what they should charge to cover their costs.

Part (a): Expected Loss Calculation

The expected loss (or cost) for the insurance company can be calculated using the probability of each outcome and the associated cost.

1. Probability of no collision = 0.95

   • Cost if no collision occurs = $0

2. Probability of collision = 0.05

   • Cost if a collision occurs = $10,500

The expected loss (E) is: $E = (0.95 \times 0) + (0.05 \times 10,500)$ $E = 0 + 525 = 525$

So, the expected loss (average loss) for the insurance company is $525.

Part (b): Insurance Premium Calculation

To break even on average, the insurance company should charge an amount equal to their expected loss, which is $525. However, insurance companies typically add a markup to cover administrative costs, profit, and other risks.

If we assume they want to charge exactly the expected loss without additional costs, they would charge $525. In practice, the actual premium might be higher to ensure profitability and cover operational costs.

---

Would you like additional details, or do you have any questions on these calculations?

Related Questions:

1. What factors could increase or decrease the insurance premium aside from the expected cost?
2. How would the expected loss change if the probability of a collision increased?
3. How might the insurance company adjust the premium if they anticipate multiple claims?
4. What is the effect of having a deductible on the expected cost and premium?
5. How does risk assessment affect the price of insurance premiums for different individuals?

Tip:

When calculating expected values in probability, remember to multiply each outcome's value by its probability and then sum these products to get the expected result.