Question

# What is the probability that a number selected from the numbers 1,2,3, ……,15 is a multiple of 4?

Hint: Here, we will be proceeding by evaluating how many numbers out of the given 15 numbers are a multiple of 4 and then the required probability is easily determined with the help of the
general formula for probability of occurrence of an event.

Given, the numbers are 1,2,3,4,5,6,7,8,9,10,11,12,13,14 and 15

As we know that the general formula for probability is given by
Probability of occurrence of an event$= \dfrac{{{\text{Number of favourable cases}}}}{{{\text{Total number of possible cases}}}}$

Here, the event is that we have to select a number from the given 15 numbers such that the selected number is a multiple of 4.

So, the favourable event is that the selected number is a multiple of 4.
From the given 15 numbers, the numbers that are multiple of 4 are 4,8 and 12.

Here, Number of favourable cases = Total number of numbers (out of the given numbers) that are multiple of 4 = 3
Total number of possible cases = Total number of given numbers = 15

Therefore, Probability that a number selected is a multiple of 4 $= \dfrac{{\text{3}}}{{{\text{15}}}} = \dfrac{1}{5}$.

Hence, $\dfrac{1}{5}$ is the probability that a number selected from the numbers 1,2,3, ……,15 is a multiple of 4.

Note: In this particular problem, the numbers which are multiple of 4 are the numbers which are exactly divisible by number 4 (i.e., the numbers which are when divided by 4 does not leave any remainder). Here, the possible cases include all the 15 given numbers because when a number is selected at random out of these 15 numbers, anyone of them can occur.