A roulette wheel has 18 red slots and 18 black slots numbered alternaetly with the numbers 1 through 36. Two green slots are numbered 0 and 00. The winning number is determined by the slot into which a single marble rolls. Players are not allowed to bet on green. The house wins all bets if 0 and 00 comes up. What are the odds against a black number winning? a. 10:9, b. 9:10, c. 1:1, d. 19:9
Including 0 and 00, there are 38 possibilities.
1 - 18/38 = 20/38 = 10/19
It doesn't seem to fit any of your alternatives. Do you or your text have a typo? If a was 10:19, it would be right.
To determine the odds against a black number winning, we need to find the number of black slots and the total number of slots on the roulette wheel.
Given:
red slots = 18
black slots = 18
green slots = 2
To find the total number of slots on the wheel, we add the number of red, black, and green slots together:
Total number of slots = red slots + black slots + green slots
Total number of slots = 18 + 18 + 2
Total number of slots = 38
The odds against a black number winning can be calculated as the ratio of the number of ways for a black number not to win to the number of ways for a black number to win.
Number of ways for a black number to win = number of black slots = 18
Number of ways for a black number not to win = total number of slots - number of black slots
Number of ways for a black number not to win = 38 - 18
Number of ways for a black number not to win = 20
So, the odds against a black number winning are 20:18, which simplifies to 10:9.
Therefore, the correct answer is a. 10:9.