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Milan is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6. The number cube

 

Milan is playing a game of chance in which he rolls a number cube with sides numbered from 1 to 6. The number cube is fair, so a side is rolled at random. This game is this: Milan rolls the number cube once. He wins $1 if a 1 is rolled, $2 if a 2 is rolled, $3 if a 3 is rolled, and $4 if a 4 is rolled. He loses $2.75 if a 5 or 6 is rolled. (If necessary, consult a list of formulas.) (a) Find the expected value of playing the game. I dollars (b) What can Milan expect in the long run, after playing the game many times? Milan can expect to gain money. He can expect to win dollars per roll. Milan can expect to lose money. He can expect to lose dollars per roll. Milan can expect to break even (neither gain nor lose money). ?

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