Heather has a bag with 8 balls numbered 1 through 8. She is playing a game of chance.
This game is this: Heather 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, and $10 if the number 6 is selected. She loses $13 if 7 or 8 is selected.(a) Find the expected value of playing the game.

(b) What can Heather expect in the long run, after playing the game many times?
(She replaces the ball in the bag each time.)

Heather can expect to gain money.

Heather can expect to lose money.

Heather can expect to break even (neither gain nor lose money).