Question

Assume that three business owners each own an identical storage building valued at $120,000.

Assume that there is a 1% chance in any year each building will be destroyed by a peril (fire), and that a loss to any of the buildings is an independent event. Assuming that:
(first case ) Fire events are independent of each other
(second case) Each building faces the same types of risks and environmental conditions.
Given that, solve the below questions for each case:
1. Use the compound probability of independent events law to find the sample space of the probability of each possible event
2. Find the annual expected loss for each of the insureds.
3. Find the risk of incurrence of losses (Std dev)

Answer 1

In the first case, we can use the compound probability of independent events law to find the sample space of the probability of each possible event. In the second case, the sample space remains the same, but the annual expected loss and risk of incurrence of losses can be calculated using the value of the building and the probability of each specific combination.

Step-by-step explanation:

In the first case, where fire events are independent of each other and each building faces the same risks and conditions, we can use the compound probability of independent events law to find the sample space of the probability of each possible event. The sample space will consist of all the possible combinations of buildings that can be destroyed by fire. Since each building has a 1% chance of being destroyed, the probability of a specific combination of buildings being destroyed is (0.01)^n, where n is the number of buildings. For example, if we have 3 buildings, the sample space would consist of {(0, 0, 0), (0, 0, 1), (0, 1, 0), (1, 0, 0), (0, 1, 1), (1, 0, 1), (1, 1, 0), (1, 1, 1)} with each combination having a probability of (0.01)^3 = 0.000001.

In the second case, where each building faces the same risks and conditions, the sample space remains the same as the first case. The annual expected loss for each insured can be calculated by multiplying the value of the building by the probability of that specific combination of buildings being destroyed. For example, if each building is valued at $120,000, the annual expected loss for the combination (0, 0, 1) would be $120,000 * 0.000001 = $0.12. The risk of incurrence of losses (standard deviation) can be calculated by finding the square root of the variance, where the variance is the sum of the squared differences between the expected loss and the actual loss for each combination of buildings.