there is a spinner with 15 equal areas, numbered 1 through 15. if the spinner is spun one time, what is the…

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 4 and a multiple of 6?

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 4 and a multiple of 6?

Answer

Explanation:

Step1: Find common - multiples

Find the least common multiple of 4 and 6. Prime - factorize: $4 = 2\times2$ and $6=2\times3$. The LCM of 4 and 6 is $2\times2\times3 = 12$.

Step2: Count favorable outcomes

The numbers on the spinner range from 1 to 15. The only number in the range 1 - 15 that is a multiple of both 4 and 6 is 12. So the number of favorable outcomes is 1.

Step3: Calculate probability

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. The total number of outcomes is 15. So $P=\frac{1}{15}$.

Answer:

$\frac{1}{15}$