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

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