1. Optimal Decision using Expected Value To determine the optimal decision, Expected Value (EV) is calculated for each location: Travers River: Probability of earthquake (E): 15% or 0.15 Probability of no earthquake (NE): 85% or 0.85 Cost of building on Travers: -$145M Cost of earthquake and rebuild on French Canyon: -$145M - $170M = -$315M EV(Travers) = (0.15 * -$315M) + (0.85 * -$145M) = -$47.25M - $123.25M = -$170.5M French Canyon: Cost of building on French Canyon: -$170M EV(French Canyon) = -$170M Since the expected cost of building on the French Canyon river is lower than the expected cost of building on the Travers river, the optimal decision is to build on the French Canyon river. 2. Sensitivity Analysis A sensitivity analysis was performed in PrecisionTree, varying the probability of the earthquake from 13% to 17%. The results show that the optimal decision changes at a probability of approximately 14.29% (0.1429). Travers River: The expected cost for the Travers River increases as the probability of an earthquake increases. This is because the higher the probability, the more likely the high-cost outcome (earthquake and rebuild) becomes, increasing the expected cost. French Canyon: The expected cost for the French Canyon remains constant at -$170M because the outcome is not dependent on the probability of an earthquake at the Travers site. Critical Probability: The critical probability is approximately 0.1429 (14.29%). Decision Change: When the probability of the