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Suppose you play a game in which a fair 6-sided die is rolled once. If...

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Suppose you play a game in which a fair 6-sided die is rolled once. If the outcome of the roll (The number of dots on the side facing upward) is a six, you win $6+m. If you roll a Three, four or five, you win $ 8+m. If you roll a one, or two, you lose $10+m.Let X be the profit from the game (or the amount of money won or lost per roll)Negative profit corresponds to lost money.a. What is the profit, X, if the outcome of the roll is 3?b. Fill out the following probability distribution table in your bookletc. Computer the mean of X, (the expected profit or loss, E(X)).d. Explain the meaning of the expected value of X in the context of this problem.e. If you played this game 100 times, how much would you expect to win or lose?

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