There is a spinner with 11 equal areas, numbered 1 through 11. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 2?
There are several ways to approach this problem, but one possible method is to use the principle of inclusion-exclusion. We start by noting that there are 5 numbers that are multiples of 2 (2, 4, 6, 8, 10) and 3 numbers that are multiples of 3 (3, 6, 9), but one of them (6) is counted twice. So there are a total of 7 numbers that are either multiples of 2 or multiples of 3.
However, we have to be careful not to count the number 6 twice. Therefore, we subtract the probability of getting 6, which is 1/11. This gives us a total probability of:
5/11 (multiples of 2) + 2/11 (multiples of 3, excluding 6) - 1/11 (multiples of 6) = 6/11
Therefore, the probability of getting a multiple of 3 or a multiple of 2 is 6/11.