A number of years ago there was a popular television game show called “Let make a...
A number of years ago there was a popular television
game show called “Let make a deal”. The host would randomly select
contestants from the audience and as the title suggests, he would
make deals for prizes. Contestants would be given relatively modest
prizes and then would be offered the opportunity to risk the prize
to win better ones.
Suppose that you are a contestant on this show. The host has just
given you a free trip worth $500 to a place that is of little
interest to you. He now offers you a trade: give up the trip in
exchange for a gamble. On the stage, there are 3 curtains, A, B,
and C. Behind one of them is a brand-new car worth $20,000. Behind
the other two curtains the stage is empty. You decide to gamble and
you select curtain A. In an attempt to make things more
interesting, the host then exposes an empty stage by opening
curtain C. (He knows that there is nothing behind curtain C.) He
then offers you the free trip again if you now quit the game or, if
you like, you can propose another deal. What do you do?
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