Question

One number is to be chosen from numbers $1$ to $100$. Then the probability that it is divisible by $5$ is…
A. $\dfrac{{33}}{{100}}$
B. $\dfrac{7}{{100}}$
C. $\dfrac{1}{5}$
D. $\dfrac{{43}}{{100}}$

Answer 1

To find the probability that the chosen number is divisible by $5$, find all numbers from 1 to 100 which are divisible by $5$. Then use the following probability formula to find the probability that the number will be divisible by 5.

• Probability of an event is given by the number of favorable outcomes divided by the total number of outcomes.

Complete step-by-step answer:
Find the total number of outcomes.
There are $100$ numbers between $1$ to $100$.
Therefore, total number of outcomes $= 100$.
Find the numbers which are divisible by $5.$
We say a number is divisible by p if on division by p the remainder comes out to be zero. So, the multiples of p are the numbers which can be taken as divisible by p.
The numbers which are divisible by $5$ are all the multiples of five from 1 to 100.
$\\{ 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100\\}$.
Therefore, number of favorable outcomes $= 20.$
Find the probability using the formula.
Probability of an event is given by the number of favorable outcomes divided by the total number of outcomes.
Here the total number of outcomes is 100 and the favorable outcome is 20.
$\Rightarrow$ Probability ${\text{ = }}\dfrac{{{\text{20}}}}{{{\text{100}}}}$
Cancel out all common factors from numerator and denominator.
$= \dfrac{1}{5}$
$\therefore$ Probability that the number is divisible by $5 = \dfrac{1}{5}$

So, the correct answer is “Option C”.

Note: Students many times make mistakes in writing probability in unsolved form, they should always keep in mind that there should be no common factor between the numerator and the denominator and the probability should be in the simplest form. Also, check that the probability value should be greater than or equal to zero and less than or equal to one. Here $\dfrac{1}{5} = 0.2$ which lies between 0 and 1.