To determine the probability that the result is a multiple of both 4 and 6 when spinning a spinner with 12 equal areas numbered from 1 to 12, follow these steps:
1. Identify the Multiples:
- First, a number must be a multiple of both 4 and 6.
- The least common multiple (LCM) of 4 and 6 is 12.
2. List the Numbers:
- The numbers on the spinner range from 1 to 12.
- So, the multiple of 12 in this range is 12 itself (as it is the smallest number that is both a multiple of 4 and 6).
3. Count Favorable Outcomes:
- The only number that meets the criteria of being a multiple of both 4 and 6 is 12.
- Therefore, there is just 1 favorable outcome.
4. Determine the Total Outcomes:
- There are a total of 12 areas on the spinner.
5. Calculate the Probability:
- The probability is the ratio of the number of favorable outcomes to the total number of possible outcomes.
- In this case, it is [tex]\( \frac{1}{12} \)[/tex].
Therefore, the probability that the result is a multiple of both 4 and 6 when the spinner is spun one time is [tex]\( \frac{1}{12} \)[/tex], which in decimal form is approximately 0.0833 (or 8.33%).
