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At a back-to-school party, one of your friends lets you play a two-stage game where...

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Geometry

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At a back-to-school party, one of your friends lets you play a two-stage game where you pay $3 to play. The game works as follows: flip a fair coin, noting the side showing, and roll a fair standard 4-sided die (numbered 1-4), noting the number showing. If the die shows a 3 and the coin shows tails, then you win $20. If the coin shows heads and the die shows an even number, then you win $7. Otherwise, you do not win anything.Let X be your net winnings.(a) Create a probability distribution for X. Enter the possible values of X in ascending order from left to right. All probabilities should be exact.(b) Compute your expected net winnings for the game. Round your answer to the nearest cent.(c) Is this game fair?YesNo

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