College playboy “Studley” Moore likes to throw lavish parties in his spacious Davis apartment. He has...

College playboy “Studley” Moore likes to throw lavish parties in his spacious Davis apartment. He has one quirk though. He insists that every guest, on their way in, play a game of “odd or even” with him. Each of the two sticks out one or two fingers, and Studley wins if the sum is even. Studley pays the guest $5 when the sum is odd (i.e., there are oneor three fingers showing), but he collects $6 when the sum is two and $4 when the sum is four. Suppose that Studley uses the strategy of sticking out one finger with probability 7/12 and two fingers with probability 5/12. Assume that each guest chooses one or two fingers with equal probability. Find the probability distribution for Studley's winnings W in a game of odd or even, and compute Studley's expected winnings in this game. Would always sticking out one finger be a better strategy for Studley (up until he gets found out)?

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College playboy “Studley” Moore likes to throw lavish parties in his spacious Davis apartment. He has...

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