Roulette wheels in Nevada have 38 pockets. They are all numbered 0, 00, and 1 through 36. Of all 38 pockets, there are 18 red, 18 are black, and 2 are green. Each time the wheel is spun, a ball lands in one of the pockets, and each pocket is equally likely.

Question

If you spin the wheel twice, what is the probability lands in a black pocket in both spins?

If you spin the wheel three times, what is the probability that the ball lands in the same pocket in all three spins?

How do I set up these problems?

Bot · Answer

To set up these problems, you can use the following steps:

1. For each case, consider the available pockets and the successful outcomes required for the given condition.
2. Find the probability for each successful outcome considering the total number of pockets.
3. If there are multiple spins as in both problems, multiply the probabilities obtained in step 2 for each of those spins.

Now let's solve each problem with these steps.

Problem 1: Probability that the ball lands in a black pocket in both spins
Step 1: There are 18 black pockets and the ball must land in one of those pockets in both spins.
Step 2: The probability for each successful outcome in one spin = number of black pockets / total number of pockets = 18/38.
Step 3: Since there are 2 spins, multiply the probabilities obtained for each spin: (18/38)*(18/38) = 324/1444 ≈ 0.224.

So the probability that the ball lands in a black pocket in both spins is about 0.224.

Problem 2: Probability that the ball lands in the same pocket in all three spins
Step 1: There are 38 pockets and the ball must land in one of those pockets in all three spins.
Step 2: The probability for each successful outcome in one spin = 1/38 (since the ball must land in a specific pocket).
Step 3: Since there are 3 spins, multiply the probabilities obtained for each spin: (1/38)*(1/38)*(1/38) = 1/54872 ≈ 0.000018.

So the probability that the ball lands in the same pocket in all three spins is about 0.000018.