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 2 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 2 or a multiple of 3?

Answer

Explanation:

Step1: Find multiples of 2

Multiples of 2 from 1 - 12 are 2, 4, 6, 8, 10, 12. So there are 6 of them.

Step2: Find multiples of 3

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

Step3: Find common multiples

Common multiples of 2 and 3 (i.e., multiples of 6) are 6, 12. There are 2 of them.

Step4: Use inclusion - exclusion principle

The number of elements that are multiples of 2 or 3 is (n(A\cup B)=n(A)+n(B)-n(A\cap B)=6 + 4-2=8).

Step5: Calculate probability

The total number of outcomes is 12. Probability (P=\frac{n(A\cup B)}{n(S)}=\frac{8}{12}=\frac{2}{3}).

Answer:

(\frac{2}{3})