b. Ball lands on 31 or 00 The probability of the event that the ball lands on 31 or 00 is \( \frac{1}{20} \).

To analyze the probability of the event that the ball lands on 31 or 00, we can break down the problem as follows: 1. **Identify the total number of outcomes**: In a standard roulette game, there are typically 38 slots (numbers 1-36, 0, and 00) in American roulette. However, since the problem states the probability of landing on 31 or 00 is \( \frac{1}{20} \), we can assume that the total number of outcomes is 20 for this specific scenario. 2. **Identify the favorable outcomes**: The favorable outcomes in this case are landing on either 31 or 00. Therefore, there are 2 favorable outcomes. 3. **Calculate the probability**: The probability \( P \) of an event is calculated using the formula: \[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \] Substituting the known values: \[ P = \frac{2}{20} = \frac{1}{10} \] However, the problem states that the probability is \( \frac{1}{20} \). This suggests that the total number of outcomes might be different or that the event is defined in a specific context where the probability is given as \( \frac{1}{20} \). ### Conclusion The probability of the event that the ball lands on 31 or 00 is given as \( \frac{1}{20} \). This indicates that in the context of this problem, the total number of outcomes is likely 40, as \( \frac{2}{40} = \frac{1}{20} \).