John has a bag with 8 balls numbered 1 through 8. He is playing a game of chance. This game is this: John chooses one ball from the bag at random. He wins $1 if the number 1 is selected, $2 if the number 2 is selected, $5 if the number 3 is selected, $6 if the number 4 is selected, $8 if the number 5 is selected, and $10 if the number 6 is selected. He loses $17 if 7 or 8 is selected. (If necessary, consult a list of formulas.) (a) Find the expected value of playing the game. dollars (b) What can John expect in the long run, after playing the game many times? (He replaces the ball in the bag each time.) O John can expect to gain money. He can expect to win dollars per selection. O John can expect to lose money. He can expect to lose dollars per selection. O John can expect to break even (neither gain nor lose money).

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