The Probability of a Roulette Wheel

An American roulette wheel has 38 slots (check here Two slots are numbered zero and double zero, and the remaining slots are numbered from one through 36. A roulette wheel looks more like this, where, again, there are 38 slots, 18 are red, 18 are black, and two are green, and the numbers are zero, double zero, and then one through 36. The way game works is, as the wheel spins, a ball bounces around, and then, wherever the ball lands determines who wins or who loses. For our problems, though, we will use this table here to help us answer the questions. This is actually where people place their bets, but it does show all of the possible outcomes.

We want to begin by determining the probability the ball lands in an odd black-numbered slot. So, looking at the table, we want to find the odd black numbers. Remember, odd numbers are one, three, five, seven, and so on. So, here, we have a black 11, a black 13, a black 15, and a black 17.

Then we have a black 29, a black 31, a black 33, and a black 35. These are the odd black slots. Notice how there are eight of them; and therefore, there are eight favorable outcomes out of a total of 38 outcomes because there are 38 slots. And therefore, the probability of the ball landing in an odd black-numbered slot is 8/38.

But this does simplify, there’s a common factor of two between eight and 38. This simplifies to 4/19, which is the exact probability. Let’s also express the probability as a decimal and a percentage. To convert to a decimal, we divide four by 19. Four divided by 19. Let’s round this to four decimal places.

The probability is approximately 0.2105, which would give us 21.05%. So the 4/19 is the exact probability. These two have been rounded. Next, we’re asked to find the probability that the ball lands on red. 18 slots are red out of the 38 slots; and therefore, the probability the ball lands on red is 18/38. Again, simplifying, we have 9/19.

Again, this is the exact probability the ball lands on red. Let’s also get our decimal approximation for this. Nine divided by 19 to four decimal places is approximately 0.4737, which would give us approximately 47.37%.

The last question is find the probability that the ball lands on zero or double zero. So, there are two favorable outcomes, either a zero or a double zero, out of a total of 38 outcomes; and therefore, the probability is 2/38, which, after simplifying, is equal to 1/19. Again, let’s convert this to a decimal. One divided by 19, Enter.

To four decimal places, we have approximately 0.0526, which is equal to 5.26%. I hope you found this helpful.