# What is the probability that a number selected at random from the set {2, 3, 7, 12, 15, 22, 72, 108}will be divisible by both 2 and 3 ?

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Given the numbers : 2, 3, 7, 12, 15, 22, 72, 108

We need to determine the probability of choosing a number divisible by 2 and 3.

Let us determine which numbers in the set are divisible by both 2 and 3.

2 ==> divisible by 2.

3 ==> divisible by 3

7 ==> None

**12** ==> divisible by 2 and 3

15 ==> divisible by 3

22 ==> divisible by 2

**72** ==> divisible by 2 and 3.

**108 **==> divisible by 2 and 3

The bold font numbers are the numbers divisible by both 2 and 3.

Then the probability of getting a number that is divisible by 2 and 3 = the total number of elements divisible by 2 and 3 / total number of elements

==> P = 3 / 8

**Then the probability is 3/8**

We have the set of numbers {2, 3, 7, 12, 15, 22, 72, 108}.

Here we see there are 8 terms in total out of which 12 , 72 and 108 or three terms are divisible by both 2 and 3.

So the probability of picking a number from the set that is divisible by both 2 and 3, is 3 / 8.

**The required probability is 3/8.**