The spiner in the photo is divided into 12 segments all numbered fro 1 to 12. That means there are a total of 12 possible outcomes for every spin. If the spinner is spun once, we want to find the probability that the outcome would be a multiple of 3. All the multiples of 3 are the expected outcomes or results of this experiment. The expected results are 3, 6, 9, and 12, which is four possible outcomes. Hence the probability of of obtaining a multiple of 3 is calculated as
P [multiple of 3] = No of expected outcomes/No of total possibilities
P [multiple of 3] = 4/12
P [multiple of 3] = 1/3
Next we note that the spinner has 6 even numbers, that is 2, 4, 6, 8, 10 and 12. The probability that the experiment yields an even number is calculated as follows;
P [even number] = No of expected outcomes/No of total possibilities
P [even number] = 6/12
p [even number] = 1/2
Therefore the probability that the spinner when spun once would result in a probability of a multiple of 3 and an even number is calculated as follows;
P [multiple of 3 and even] = P[multiple of 3] * P[even number]
P[multiple of 3 and even] = 1/3 * 1/2
P[multiple of 3 and even] = 1/6
The correct answer is Option B