Chuck-a-Luck Probability

Recall the set of payoffs in a game of chuck-a-luck:

• You win one times your bet if your number appears on one die.
• You win two times your bet if your number appears on two dice.
• You win three times your bet if your number appears on three dice
• You lose your bet if your number appears on none of the dice.

You play 50 consecutive games of chuck-a-luck, betting 5 chips in each of the first 30 games, and 10 chips in each of the remaining 20 games. By the end of these games you’ll expect to:

(Hint: You might want to draw a tree diagram to figure this one out. Note: you can win or lose to 1/10th of a chip.) <— ( I dont need the tree diagram just the answer)

A. Lose 19.5 chips

B. Lose 27.3 chips

C. Won 20.4 chips

D. break even

E. Lose 34.1 chips