Question

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 1

Multiples of 2: 2,4,6,8,10,12 (6 numbers).
Multiples of 3: 3,6,9,12 (4 numbers).
Multiples of both (6): 6,12 (2 numbers).

By inclusion–exclusion: 6 + 4 − 2 = 8 favorable outcomes out of 12, so the probability is 8/12 = 2/3.