Probability and Risk-Taking In the TV game show, "Let's Make a Deal" there are fifty briefcases that a contestant must c

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Probability and Risk-Taking
In the TV game show, "Let's Make a Deal" there are fiftybriefcases that a contestant must choose one from. The case thecontestant chooses has a check ranging from $.01 to $1,000,000inside the case, but the contestant does not know what amount is inhis or her case. Each other case is opened one after theother and "a mysterious banker" makes offers to the contestant tobuy his or her case for the amount the banker believes it is worthbased on the monetary amounts that are left. Put yourself in theshoes of the contestant and there are only two cases left, the oneyou chose at the start and one other. --- One case has a million dollars inside and the other has onecent. The banker offers you $250,000 for yourcase. If you have the penny and sell it to thebanker you'll have made an enormous sum of money, if youhad the million-dollar case and sell it to him you will havelost $750,000. Conversely, if you had the penny and kept ityou will lose everything and if you keep the million-dollar caseyou'll win a million dollars.What choice do you make? For what reasons do you make yourchoice? --- Here is another situation. What if the stakes were changed.What if the two cases left are $25 and $50 and the banker offersyou $30 for your case? What decision do you make now? Does it staythe same or change?
Please expound on all your reasonings. In discussing yourreasons make sure to include statistical principles/ideas that youused in making your decision.