O Counting and Probability WOOD 35 Nathan Computing expected value in a game of chance Greg has a bag with 8 balls numbered 1 through 8. He is playing a game of chance. This game is this: Greg chooses one ball from the bag at random. He wins $1 if the number 1 is selected, $2 if the number 2 is selected, $3 if the number 3 is selected, $4 if the number 4 is selected, and $5 if the number 5 is selected. He loses $7 if 6, 7, or 8 is selected. (a) Find the expected value of playing the game. dollars (b) What can Greg expect in the long run, after playing the game many times? (He replaces the ball in the bag each time.) Greg can expect to gain money. He can expect to win ] dollars per selection. O Greg can expect to lose money. He can expect to lose dollars per selection. Q Greg can expect to break even (neither gain nor lose money). X