Question

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 3 and a multiple of 5?

Explanation:

Step1: Find LCM of 3 and 5

The least common multiple (LCM) of 3 and 5 is \( 3\times5 = 15 \) since they are coprime. So we need to find numbers between 1 and 15 that are multiples of 15.

Step2: Identify multiples of 15 in 1 - 15

In the range 1 to 15, the only multiple of 15 is 15 itself. So there is 1 favorable outcome.

Step3: Calculate total number of outcomes

The spinner has 15 equal areas, so total number of possible outcomes is 15.

Step4: Calculate probability

Probability \( P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{1}{15} \)

Answer:

\(\frac{1}{15}\)