Roulette. A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36.

The slots 0 and 00 are colored green, 18 of the others are red, and 18 are black.

The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully balanced so that the ball is equally likely to land in any slot when the wheel slows. Gamblers can bet on various combinations of numbers and colors.

(a) What is the probability of any one of the 38 possible outcomes? Explain your answer.

(b) If you bet on “red,” you win if the ball lands in a red slot. What is the probability of winning?

(c) The slot numbers are laid out on a board on which gamblers place their bets.

One column of numbers on the board contains all multiples of 3, that is, 3, 6, 9, . . . , 36. You place a “column bet” that wins if any of these numbers comes up.

What is your probability of winning?