17-2 Game Show Uncertainty In the final round of a TV game show, contestants have a chance to increase their current winnings of 1 million dollars to 10 million dollars. If they are wrong, their prize is decreased to $100,000. To win, they have to guess the exact percentage that answered a question a certain way, and the range has already been narrowed to an 11-point range. So, for example, the contestant knows that the correct answer is between 20% and 30% and he or she must guess the correct percentage in that range. So, let's say you have no idea what the right answer is and have to make a random guess. Should you play? CHAPTER 17 MAKING DECISIONS WITH UNCERTAINTY 231 17-3 Boat Insurance Maritime Insurance Company offers insurance policies for recreational boats. A typical policy will pay the replacement cost of $25,000 if the boat is a total loss. If the boat is not a total loss but the damage is more than $10,000, the policy pays $5,000. For damage under $10,000, no coverage is offered. The company estimates the probability of no damage to be 0.60, the probability of damage between $0 and $10,000 to be 0.25, and the probability of damage between $10,000 and $25,000 to be 0.12. If the company wants to make a profit of $200 above the expected cost, what should be the price of the policy?