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What is the lowest probability of a correct guess that

Game Show Uncertainty

In the final round of a TV game show, contestants have a chance to increase their current winnings of $1 million to $2 million. If they are wrong, their prize is decreased to $500,000. A contestant thinks His guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?

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