Question 8.91

60. An American roulette wheel has 38 slots numbered 0, 00, and 1 to 36. The ball is equally likely to come to rest in any of these slots when the wheel is spun. The slot numbers are laid out on a board on which gamblers place their bets. One column of numbers on the board contains multiples of 3—that is, 3, 6, 9,…, 36. Joe places a $1 “column bet” that pays out $3 (so he gains $2) if any of these numbers comes up.

  1. What is the probability model for the outcome of one bet, taking into account the $1 cost of a bet?
  2. What are the mean and standard deviation for this model?
  3. Joe has played roulette every day for years. What does the law of large numbers tell us about his results?