There is a spinner with 14 equal areas, numbered 1 through 14. If the spinner is spun one time, what is the probability that the result is a multiple of 4 or a multiple of 6?
Question
There is a spinner with 14 equal areas, numbered 1 through 14. If the spinner is spun one time, what is the probability that the result is a multiple of 4 or a multiple of 6?
Solution
To solve this problem, we first need to identify the numbers on the spinner that are multiples of 4 or 6.
The multiples of 4 between 1 and 14 are: 4, 8, 12. That's 3 numbers.
The multiples of 6 between 1 and 14 are: 6, 12. That's 2 numbers.
However, we can see that 12 is a common multiple of both 4 and 6, so we should only count it once.
So, in total, there are 4 numbers (4, 8, 6, and 12) on the spinner that are multiples of 4 or 6.
The probability of spinning a multiple of 4 or 6 is therefore the number of favorable outcomes (multiples of 4 or 6) divided by the total number of outcomes (all the numbers on the spinner).
So, the probability is 4 (favorable outcomes) divided by 14 (total outcomes), which simplifies to 2/7.
So, the probability that the result is a multiple of 4 or a multiple of 6 when the spinner is spun one time is 2/7.
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