Q4.(15 points) Hydro Quebec, the provincial electrical utility, is trying to decide whether to replace the PCB transformer in a power generating station with a new and safer one. To evaluate this decision, Hydro Quebec needs information about the likelihood of an incident such as a fire, the cost of such an incident and the cost of replacing the transformer. Suppose the total cost of replacement is $75,000. If the transformer is replaced, there is virtually no chance of a fire. However, if the current transformer is retained, the probability of a fire is assessed to be 0.0025. If a fire occurs, then the clean-up cost could be high ($80 million) or low ($5 million). The probability of a high clean-up cost, given a fire occurs, is assessed to be 0.2.

a) Should Hydro Quebec replace the transformer?

b) Perform sensitivity analysis to the probability of a fire. Does the optimal decision from part (a) remain optimal for a wide range of values for this probability?

2. The Workers Compensation Board of Ontario receives claims from injured workers for support. Some of the claims convert from short-term disability (STD) to long-term disability (LTD), which costa a lot more. So early detection of these cases helps reduce the costs. A research study was done to find out a way to classify the claims into high risk (of conversion) and low risk (of conversion). The factors identified were the average age of worker and the number of days for STD, given age of worker, were determined based on costs and historical data. Given the determined classification rule, the data (number of claims for a specific period) was classified as follows:

	Claim converts	Does not convert
Classified as high risk	3,580	13,396
Classified s low risk	1,479	140,645

a) If a worker in Ontario is classified as high risk, what is the probability that his/her claim converts?

b) If a worker in Ontario is classified as low risk, what is the probability that his/her claim does not convert?