3. (3 points) The Federal Crop Insurance Corporation (FCIC) protect farmers against crop losses caused by the vagaries of weather: If farmers default, FCIC pays back any debt borrowed from a bank on behalf of the defaulted farmer. FCIC has relatively few inspectors to inspect individual claims. A farmer in Arizona has a choice between planting water-hungry crop and hardy crop. Both crops cost $50. The gross returns on these plants depend on the annual rainfall. For water-hungry crop, the gross return is $100 if the annual rainfall exceeds 12 inch (50\% probability), and is $0 if the annual rainfall is less than 12 inch (50\% probability). For hardy crop, the gross return is $60 if the annual rainfall exceeds 12 inch (50\% probability), and is $50 if the annual rainfall is less than 12 inch (50\% probability). Suppose a farmer borrows debt (pay back the borrowed amount, or everything he has if the cash flow is smaller than the borrowed amount) from a bank to finance the cost of planting crops. In case of farmer's default, the bank gets paid by FCIC. Which plant will the farmer choose? Why (show farmers profit for each crop)