in a certain dice game, three fair dice are rolled and the total on all three dice is counted. Let the random variable x be the total count on all three dice. construct the probability distribution for x. In the game described, you pay two dollars to roll the dice. If you roll a 16 or greater, you will win $15. If you roll a 6 or lower, you win $8. If you roll anything else, you lose your money. What is the expected value of this game?

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