Question

a spinner from 1-6
what the theoretical probability of spinning a 1
what the theoretical probability of spinning an odd number
what the theoretical probability of spinning a 9

Answer 1

To calculate the theoretical probabilities, we need to know the total number of outcomes as well as the number of favorable outcomes for each scenario.

1. **Theoretical probability of spinning a 1**:
- Total outcomes: 6 (the numbers 1, 2, 3, 4, 5, 6)
- Favorable outcomes: 1 (only the number 1)
- Probability = Favorable Outcomes / Total Outcomes = 1/6

2. **Theoretical probability of spinning an odd number**:
- Odd numbers in the range 1-6: 1, 3, 5
- Total outcomes: 6
- Favorable outcomes: 3 (the numbers 1, 3, and 5)
- Probability = 3/6 = 1/2

3. **Theoretical probability of spinning a 9**:
- The number 9 is not included in the spinner (which only has numbers 1 through 6).
- Total outcomes: 6
- Favorable outcomes: 0 (since 9 is not in the range)
- Probability = 0/6 = 0

In summary:
- Probability of spinning a 1: \( \frac{1}{6} \)
- Probability of spinning an odd number: \( \frac{1}{2} \)
- Probability of spinning a 9: \( 0 \)