Question

A die is rolled once. What is the probability of rolling a prime number?
a. $\dfrac{2}{3}$
b. $\dfrac{1}{2}$
c. $\dfrac{1}{6}$
d. $\dfrac{5}{6}$

Answer 1

We have to take reference of prime numbers and on the basis of this, we will first find the prime numbers between 1 and 6, that are, 2, 3 and 5. Then, we will find the probability using the formula, $\text{Probability=}\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$. Here, favourable outcomes are 2, 3, 5 and the total number of outcomes are 6.

Complete step-by-step answer:
It is given in the question that, a die is rolled once and we have been asked to find the probability that it is a prime number.
So, first let understand what prime numbers are. They are the numbers having only 2 factors, which are 1 and the number itself. Examples of prime numbers are 2, 3, 5, 7, 11, etc.
Now, we know that in a die there are a total of 6 faces, named as 1, 2, 3, 4, 5, 6 and out of these the prime numbers are 2, 3 and 5.
Hence, we will get the number of favourable outcomes as 3, that is, 2, 3 and 5.
And we also know that the total number of outcomes is 6.
We know that probability can be found out using the formula, $\text{Probability=}\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
So, the probability of rolling a prime number will be,
$\text{Probability=}\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}=\dfrac{3}{6}=\dfrac{1}{2}$
Hence, we get the probability of rolling a prime number as $\dfrac{1}{2}$.
Therefore, option (b) is the correct answer.

Note: Most of the students make a mistake thinking that 1 is also a prime number and as a result, they get the answer as $\dfrac{4}{6}=\dfrac{2}{3}$ and end up writing option (a) as the correct answer, but this is wrong. It is because 1 is not a prime number. The smallest prime number is 2.