Jina has a bag with 8 balls numbered 1 through 8 . She is playing a game of chance. This game is this: Jina chooses one ball from the bag at random. She 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, \( \$ 10 \) if the number 6 is selected. She loses \( \$ 14 \) if 7 or 8 is selected. (a) Find the expected value of playing the game. dollars (b) What can Jina expect in the long run, after playing the game many times? (She replaces the ball in the bag each time.) She can expect to win \( \square \) dollars per selection. She can expect to lose money. Oina can expect to break even (neither gain nor lose money).
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