O Counting and Probability [ | i 1 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 !9' selected, $4 if the number 4 is selected, and $35 if the number 5 is selected. H e loses $7 if 6, 7, or 8 is selected. () Find the expected value of playing the game. [ dotiars : s X (b) What can Greg expect in the long run, after playing the game many times? (He replaces the ball in the bag each time.) O Greg can expect to gain money. He can expect to win D dollars per selection. O Greg can expect to lose money. He can expect to lose U dollars per selection. Q Greg can expect to break even (neither gain nor lose money)