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

Answer

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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.

Complete step-by-step answer:

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.

general formula for probability of occurrence of an event.

Complete step-by-step answer:

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.

Last updated date: 20th Sep 2023

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