"Three dice are rolled in a wire cage. You place a bet on any number from 1 to 6. If any one of the three dice comes up with your number, you win the amount of your bet. (You also get your original stake back.) If more than one die comes up with your number, you win the amount of your bet for each match. For example, if you had a $1 bet on number 5, and each of the three dice came up with 5, you would win $3 a. What is the probability that the gambler wins the game? b. Who has the long-run advantage in the game; the house or the gambler? By how much on the dollar? c. How would you change the amount of the winnings in every round of Chuck-a-Luck to make the game fair? Say that doubles pay Sa per $1 bet rather than $2 and triples pay $b per $1 bet instead of $3. What is the condition on a and b