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 2 or a multiple of 5?
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 2 or a multiple of 5?
Solution
To solve this problem, we first need to identify the numbers that are multiples of 2 or 5 within the range of 1 to 14.
The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14. That's 7 numbers.
The multiples of 5 are: 5, 10. That's 2 numbers.
However, we have to be careful not to double count the number 10, which is a multiple of both 2 and 5. So, in total, we have 7 (multiples of 2) + 2 (multiples of 5) - 1 (the overlap, 10) = 8 favorable outcomes.
The total number of outcomes is 14 (since the spinner has 14 equal areas).
So, the probability of the spinner landing on a number that is a multiple of 2 or 5 is the number of favorable outcomes divided by the total number of outcomes, which is 8/14 = 4/7.
So, the probability is 4/7.
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