1. **State the problem:** We have a spinner divided into 12 equal sections numbered 1 through 12. We want to find the probability that the spinner lands on a number that is a multiple of 5 or a multiple of 2. 2. **Formula and rules:** The probability of an event is given by: $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ When finding the probability of "A or B" (union of two events), use the formula: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ where $P(A \cap B)$ is the probability of both events happening (intersection). 3. **Identify multiples:** - Multiples of 5 between 1 and 12: 5, 10 - Multiples of 2 between 1 and 12: 2, 4, 6, 8, 10, 12 4. **Count favorable outcomes:** - Multiples of 5: 2 numbers - Multiples of 2: 6 numbers - Multiples of both 5 and 2 (intersection): 10 (1 number) 5. **Calculate probability:** $$P(\text{multiple of 5 or 2}) = \frac{2}{12} + \frac{6}{12} - \frac{1}{12} = \frac{2 + 6 - 1}{12} = \frac{7}{12}$$ 6. **Final answer:** The probability that the spinner lands on a multiple of 5 or 2 is **$\frac{7}{12}$**.