In the Movie Casablanca, Rick played by Humpy Bogart, helped a married couple by allowing the husband to win at the Roulette table when he bet on the number 22, 3 times in a row.
Assume the Roulette table contained a rotating wheel with 38 slots, numbered 1 through 38, and the rolling ball was equally likely to land on any one of the 38 slots.
What is the Probability of the number 22 randomly coming up 3 times in a row?
If the net payoff (net gain) is 35 dollars for each dollar bet how much money would the husband win if he bet $10.00 on the first roll and left his winning on the number 22 for the next two spins?