Question
Question There is a spinner with 13 equal areas, numbered 1 through 13 . If the spinner is spun one time, what is the probability that the result is a multiple of 2 and a multiple of 3 ?
Ask by Park Elliott.
Feb 02,2025 21:25
UpStudy AI Solution
Tutor-Verified Answer
Answer
The probability is 2⁄13.
Solution
To determine the probability that the spinner lands on a number that is both a multiple of 2 and a multiple of 3, follow these steps:
1. **Identify the Total Possible Outcomes:**
- The spinner has 13 equal areas, numbered from 1 to 13.
- Therefore, there are **13 possible outcomes**.
2. **Determine the Numbers that are Multiples of Both 2 and 3:**
- A number that is a multiple of both 2 and 3 is a multiple of **6** (since 6 is the least common multiple of 2 and 3).
- Within the range of 1 to 13, the multiples of 6 are:
- **6 and 12**
3. **Count the Favorable Outcomes:**
- There are **2 favorable outcomes** (6 and 12).
4. **Calculate the Probability:**
\[
\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{2}{13}
\]
**Final Answer:**
The probability is 2⁄13.
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Simplify this solution Beyond the Answer
To determine the probability that the result of a spin is a multiple of both 2 and 3, we first need to identify the common multiples of these numbers within the range of 1 to 13. The least common multiple of 2 and 3 is 6. Therefore, the only multiples of 6 between 1 and 13 is 6 itself. So, there is 1 favorable outcome (6) out of 13 possible outcomes. Hence, the probability is 1/13.
To put this in simpler terms, you have 13 slices on the spinner. If you want to land on a slice that is both even and a multiple of 3, you're really looking for the magical number 6! Just one little slice from all those 13 holds the key, making your chance of landing on it a neat 1 out of 13. Spin away, and may the odds be ever in your favor!
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