Question 315170: Consider a state lottery that has a weekly television show. On this show, a contestant receives the opportunity to win $1 million. The contestant picks from four hidden windows. Behind each is one of the following: $150,000, $200,000, $1 million, or a "stopper". Before beginning, the contestant is offered $100,000 to stop. Mathematically speaking, should the contestant take the $100,000?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Consider a state lottery that has a weekly television show.
On this show, a contestant receives the opportunity to win $1 million.
The contestant picks from four hidden windows.
Behind each is one of the following: $150,000, $200,000, $1 million, or a "stopper".
Before beginning, the contestant is offered $100,000 to stop.
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Let random variable X be the players gain over 100,000 if he plays.
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X Values: 50,000, 100,000, 900,000, 0
Probs:::: 1/4, 1/4, 1/4, 1/4
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E(x) = (1/4)(50,000+ 100,000+ 900,000+ 0) = 262,500
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Mathematically speaking, should the contestant take the $100,000?
Absolutely Not.
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Cheers,
Stan H.
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