1. The problem states that Brian wants to insure a painting against theft with a probability of theft $p = 0.02$ during the year. 2. The insurance policy covers a loss of $10,000 if the painting is stolen. 3. The expected loss (or expected value of the theft) is calculated by multiplying the probability of theft by the loss amount: $$\text{Expected loss} = p \times \text{Loss} = 0.02 \times 10,000 = 200$$ 4. This expected loss represents the fair price Brian should be willing to pay for the insurance policy to break even on average. 5. Therefore, Brian should be willing to pay up to $200 for the insurance policy.