There is a spinner with 15 equal areas, numbered 1 through 15. If the spinner is spun one time, what is the probability that the result is a multiple of 5 or a multiple of 3?
There are five multiples of 3 (3, 6, 9, 12, 15) and three multiples of 5 (5, 10, 15) among the 15 numbers on the spinner. However, 15 is counted twice since it is both a multiple of 3 and a multiple of 5, so we need to subtract one from the total count.
Therefore, the probability of getting a multiple of 5 or a multiple of 3 is:
$$P(\text{multiple of 3 or 5}) = \frac{5+3-1}{15} = \frac{7}{15}$$
So the probability is $\boxed{\frac{7}{15}}$.
To find the probability of the spinner landing on a multiple of 5 or a multiple of 3, we need to determine the number of favorable outcomes (the numbers that are multiples of 5 or 3) and the total number of possible outcomes.
First, let's identify the multiples of 5 from 1 to 15: 5, 10, and 15.
Next, let's identify the multiples of 3 from 1 to 15: 3, 6, 9, 12, and 15.
We observe that the number 15 is counted in both sets because it is a multiple of both 5 and 3.
Now, let's find the total number of possible outcomes, which is the number of equal areas on the spinner, which is 15.
The favorable outcomes are: {3, 5, 6, 9, 10, 12, 15}.
Thus, the number of favorable outcomes is 7.
Finally, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes
Probability = 7 / 15
So, the probability that the spinner will result in a multiple of 5 or a multiple of 3 is 7/15.