Final answer:
To compute the probability of winning these bets, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes. For betting on a color, the probability is 9/19, and for betting on one of the dozen groups, the probability is 6/19.
Step-by-step explanation:
To compute the probability of winning these types of bets, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
a. Betting on a color: In an American roulette wheel, there are 18 red numbers, 18 black numbers, and 2 green numbers. So, the probability of winning by betting on a color is 18/38 or 9/19.
b. Betting on one of the dozen groups: There are 12 numbers in each dozen group. So, the probability of winning by betting on one of the dozen groups is 12/38 or 6/19.