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Flip four fair coins and win $1 for each head. You may flip the tails again once. What is the expected value of the game?

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You flip four fair coins and win $1 per head, and may re-flip a single coin of your choice. Playing rationally, what is your expected profit?Four fair coins pay $1 per head. You may re-flip all four once but must keep the second result. What is the game worth?Flip 100 coins and multiply the number of heads by the number of tails. What is the expected value of the product? Give a confidence interval for it.

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