Answer:
[tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
Probability is the measure of the likelihood that an event will occur, and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
[tex]\boxed{\textsf{Probability}=\dfrac{\textsf{Number of favorable outcomes}}{\textsf{Total number of possible outcomes}}}}[/tex]
Given that a spinner has 12 equal areas numbered 1 through 12, the total number of possible outcomes is 12.
To find the probability that the result of spinning the spinner one time is a multiple of 2 or a multiple of 3, we need to count the outcomes that satisfy either condition and then divide by the total number of possible outcomes.
Multiples of 2: 2, 4, 6, 8, 10, 12
Multiples of 3: 3, 6, 9, 12
Since the numbers 6 and 12 appear in both lists, we only need to count them once. So, there is a total of 8 favourable outcomes:
2, 3, 4, 6, 8, 9, 10, 12
Therefore:
[tex]\textsf{Probability} = \dfrac{\textsf{Number of favorable outcomes}}{\textsf{Total number of outcomes}} = \dfrac{8}{12} = \dfrac{2}{3}[/tex]
So, the probability that the result is a multiple of 2 or a multiple of 3 is:
[tex]\dfrac{2}{3}[/tex]
