there is a spinner with 12 equal areas, numbered 1 through 12. if the spinner is spun one time, what is the…

there is a spinner with 12 equal areas, numbered 1 through 12. if the spinner is spun one time, what is the probability that the result is a multiple of 4 or a multiple of 3?

there is a spinner with 12 equal areas, numbered 1 through 12. if the spinner is spun one time, what is the probability that the result is a multiple of 4 or a multiple of 3?

Answer

Explanation:

Step1: Find multiples of 4

Multiples of 4 from 1 - 12 are 4, 8, 12. So there are 3.

Step2: Find multiples of 3

Multiples of 3 from 1 - 12 are 3, 6, 9, 12. So there are 4.

Step3: Find common multiples

Common multiples of 3 and 4 (i.e., multiples of 12) from 1 - 12 is 12. There is 1.

Step4: Use inclusion - exclusion principle

The number of elements that are multiples of 4 or 3 is $3 + 4- 1=6$.

Step5: Calculate probability

The total number of outcomes is 12. Probability $P=\frac{6}{12}=\frac{1}{2}$.

Answer:

$\frac{1}{2}$