there is a spinner with 14 equal areas, numbered 1 through 14. if the spinner is spun one time, what is the…

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 3 and a multiple of 4?

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 3 and a multiple of 4?

Answer

Explanation:

Step1: Find common - multiples

First, find the multiples of 3 from 1 to 14: 3, 6, 9, 12. Then find the multiples of 4 from 1 to 14: 4, 8, 12. The common multiple of 3 and 4 from 1 to 14 is 12 (since the least - common multiple of 3 and 4 is 12). So there is 1 number that is a multiple of 3 and a multiple of 4 in the set {1, 2, …, 14}.

Step2: Calculate probability

The probability formula is $P(A)=\frac{n(A)}{n(S)}$, where $n(A)$ is the number of favorable outcomes and $n(S)$ is the total number of outcomes. Here, $n(A) = 1$ (the number 12) and $n(S)=14$ (the 14 equal - areas on the spinner). So $P=\frac{1}{14}$.

Answer:

$\frac{1}{14}$