1. Determine the after-tax expected value of the house without insurance. If the tax is always collected, the house is worth 480 = 500 - 20 if it does not burn and -20 if it does burn. Thus, the expected value of the house is 380 = [0.2 * (-20)] + [0.8 * 480].

If the tax is collected only if the fire does not occur, the expected value of the house is 384 = [0.2 * 0] + [0.8 * 480].