Question

A ticket is drawn from a bag containing $100$ tickets. The tickets are numbered from one to hundred. What is the probability of getting a ticket with a number divisible by $10$?
A. $\dfrac{1}{{10}}$
B. $\dfrac{1}{5}$
C. $\dfrac{1}{{20}}$
D. None

Answer 1

Hint: To find the probability, first we will write the sample space $S$ for tickets. Then, we will consider the event $E$ that gets a ticket with a number divisible by $10$. We will find the required probability by using the definition. That is, required probability $ = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}$ where $n\left( E \right)$ is the number of favourable (desired) outcomes and $n\left( S \right)$ is the number of total outcomes.

Complete step-by-step solution:
In this problem, it is given that a bag containing $100$ tickets and the tickets are numbered from one to hundred. So, one can get a ticket with a number between $1$ and $100$. The sample space is the set of all possible outcomes. Therefore, in this problem sample space for tickets is $S = \left\{ {1,2,3,...,100} \right\}$. Therefore, $n\left( S \right) = 100$.
Now we will consider the event $E$ that gets a ticket with a number divisible by $10$. That is, our desired outcome is a number divisible by $10$. We know that between $1$ and $100$, the numbers $10,20,30,40,50,60,70,80,90,100$ are divisible by $10$. We can see that these are $10$ numbers. Therefore, $n\left( E \right) = 10$.
Now we are going to find the probability of an event $E$ by using the definition. That is, $P\left( E \right) = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}$.
$ \Rightarrow P\left( E \right) = \dfrac{{10}}{{100}}$
$ \Rightarrow P\left( E \right) = \dfrac{1}{{10}}$
Hence, the probability that getting a ticket with a number divisible by $10$ is $\dfrac{1}{{10}}$.

Hence, option A is the correct answer.

Note: In this problem, if we have to find the probability that getting a ticket with a number whose unit digit $0$ then the answer will be the same. That is, probability of getting a ticket with a number whose unit digit $0$ is also $\dfrac{1}{{10}}$. In this problem, if we have to find the probability of getting a ticket with a multiple of $10$ then the answer will be the same. That is, the probability of getting a ticket with a number multiple of $10$ is also $\dfrac{1}{{10}}$.