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 ?

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