8. Decision Tree [modified from Meredith et al, 1973]. A spillway for a dam is to be constructed. The choices are to build a small spillway costing $2 million or a large spillway costing $3 million. Flood occurrence records for this site show that during the projected design lifetime of the dam, there is a 0.25 probability that a serious flood will occur, and a 0.10 probability that a major flood will occur. Dam failure from a serious flood has a 0.70 probability of causing $6 million damages and a 0.30 probability of causing $8 million damages. Dam failure from a major flood has a 0.70 probability of causing $8 million damages and a 0.30 probability of causing $10 million damages. The probabilities that that the two possible spillway types will fail during the two levels of flood are as follows: serious flood major flood Spillway large small fail 0.05 0.10 safe 0.95 0.90 fail 0.10 0.25 safe 0.90 0.75 a. Construct and label the decision tree. If multiple pages are needed, clearly label corresponding branches. b. What is the best choice based on EMV? c. Describe two cautionary statements about using such an EMV choice, using twenty or fewer words in each case (longer answers will be penalized)