There is a spinner with 13 equal areas, numbered 1 through 13. If the spinner is spun one time, what is the probability that the result is a multiple of 3 or a multiple of 2?

8/13

Step-by-step explanation:

Now the spinner has a areas - 1,2,3,4,5,6,7,8,9,10,11,12 and 13.

When we say multiples of 3, we are actually referring to those numbers that 3 can divide. For example, 8 is a multiple of 2, 15 is a multiple of 5, 14 is a multiple of 7, 36 is a multiple of 6 and so on.

We are required to find the probability that the result of the spin is either a multiple of 3 or multiple of 2. Let us extract the multiples of 2 from 1 to 13. The multiples of 2 or the numbers that can be divided by 2 from 1 to 13 are:

2,4,6,8,10, and 12. They are six in number. Since the total equal areas on the spinner are 13, then the probability that the result of the spin is a multiple of 2 is = 6/13. This is P (A).

Again, we extract the multiples of 3 from the list 1 to 13:

3,6,9,12. The multiples of 3 from 1 to 13 are four in number. Therefore the probability that the result of the spin is a multiple of 3 is = 4/3. This is P (B)

We can see that the two events are not mutually exclusive events. That is, there are some form of relationship between the two events. A further look at the two events will reveal that there are multiples of 2 that are equally multiples of 3 as well. In probability, it is written as P (A∩B). Where A represents the multiples of 2 and B will be the multiples of 3.

(A∩B) = {6,12}

Since there are two outcomes that can be found in both events, then P (A∩B) = 2/13

The probability that the result is either a multiple of 2 or multiple of 3 = P (A) + P (B) - P (A∩B)

= (6/13) + (4/13) - (2/13)

= 8/13