DB1: Probability and Risk Taking 39 39 Probability and Risk Taking In the TV game show, "Let's Make a Deal" there are fifty briefcases that a contestant must choose one from. The case the contestant chooses has a check ranging from $.01 to $1,000,000 inside the case, but the contestant does not know what amount is in his or her case. Each other case is opened one after the other and "a mysterious banker" makes offers to the contestant to buy his or her case for the amount the banker believes it is worth be based on the monetary amounts that are left. Put yourself in the shoes of the contestant and there are only two cases left, the one you chose at the start and one other. One case has a million dollars inside and the other has one cent. The banker offers you $250,000 for your case. If you have the penny and sell it to the banker you'll have made an enormous sum of money, if you had the million dollar case and sell it to him you will have lost $750,000. Conversely, if you had the penny and kept it you will lose everything and if you keep the million dollar case you'll win a million dollars. What choice do you make? For what reasons do you make your choice? Here is another situation. What if the stakes were changed. What if the two cases left are $25 and $50 and the banker offers you $30 for your case? What decision do you make now? Does it stay the same or change? Please expound on all your reasonings . In discussing your reasons make sure to include statistical principles/ideas that you used in making your decision