Question

A die is rolled. Find the probability that an odd number is obtained.

Answer 1

Here, we will be using the concept of probability to solve the question. The probability of an event is the chance that the event occurs. Odd numbers are the natural numbers which are not divisible by 2. First, we will find the total number of outcomes when a die is rolled. We will then find the favourable outcomes of getting an odd number. We will substitute the values in the formula of probability to find the answer.
Formula Used: We will use the formula for probability of an event, $P\left( E \right) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of total outcomes}}}}$.

Complete step by step solution:
First, we will find the total number of outcomes and the number of favourable outcomes.
When a die is rolled, the possible outcomes are 1, 2, 3, 4, 5, or 6 appears on the die.
Thus, we observe that the total number of outcomes is 6 when a die is rolled.
Now, we need to find the probability that an odd number is obtained.
Odd numbers are the natural numbers that are not divisible by 2. For example, 1, 3, 5, 7 are odd numbers.
We can see that the possible odd numbers when a die is rolled are 1, 3, and 5.
Therefore, we observe that the number of favourable outcomes is 3.
Next, we know that the probability of an event $E$ is given by $P\left( E \right) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of total outcomes}}}}$.
Let $E$ be the event of getting an odd number when a die is thrown.
Substituting 3 for the number of favourable outcomes and 6 for the number of total outcomes, we get
$P\left( E \right) = \dfrac{3}{6}$
Simplifying the expression, we get
$P\left( E \right) = \dfrac{1}{2}$

$\therefore$ The probability of getting an odd number when a die is thrown is $\dfrac{1}{2}$ or $0.5$.

Note:
We can also solve this problem by finding the probability of getting an even number when a die is rolled. Then, subtract it from 1 to get the probability of getting an odd number.
Even numbers are the natural numbers that are divisible by 2.
We can see that the possible even numbers when a die is rolled are 2, 4, and 6.
Therefore, we observe that the number of favourable outcomes is 3.
Next, we know that the probability of an event $E$ is given by $P\left( E \right) = \dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Number of total outcomes}}}}$.
Let $E$ be the event of getting an even number when a die is thrown.
Substituting 3 for the number of favourable outcomes and 6 for the number of total outcomes, we get
$P\left( E \right) = \dfrac{3}{6}$
Simplifying the expression, we get
$P\left( E \right) = \dfrac{1}{2}$
Therefore, we get the probability of getting an even number when a die is thrown as $\dfrac{1}{2}$.
Now, we will subtract the probability of getting an even number from 1 to get the probability of getting an odd number.
Let $O$ be the event of getting an odd number when a die is thrown.
$\begin{array}{l}P\left( O \right) = 1 - P\left( E \right)\\\ = 1 - \dfrac{1}{2}\\\ = \dfrac{1}{2}\end{array}$
Therefore, the probability of getting an odd number when a die is thrown is $\dfrac{1}{2}$ or $0.5$.