6. (7 pts) A museum wonders whether it should enter an insurance contract to prevent loss from thief. Of course, not entering any contract is also an option. The total worth of the museum pieces is estimated to be around $20,000. From statistics, around 3% chance the museum will be visited by thief in the coming year. In case the museum is broken, 60% chance the losses would be 10% of the total worth, while 40% chance the losses would be 30% of the total worth. Company A's policy costs $140 a year but guarantees to refund all losses due to theft. Company B's policy is only $100 a year, but the museum has to pay the first $60 of any loss themselves. Assume that there will be at most one theft a year. Draw the decision tree to minimize expected loss and decide what to do. Show your calculations