Question

A die is thrown once. Find the probability of getting a prime number.

Answer 1

Hint: First, start by defining probability and state the formula that probability of an event is the number of favourable outcomes divided by the total number of possible outcomes. Find the elements of the sample space and then find the favourable outcomes. Then use the above formula to arrive at the final answer.

Complete step-by-step answer:
In this question, we are given that a die is thrown once.

We need to find the probability of getting a prime number.

First, let us see the definition of probability.

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true. Probability is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility and 1 indicates certainty.

The formula for probability of an event is the number of favourable outcomes divided by the total number of possible outcomes.

The set of the total number of possible outcomes is called the sample space. So, the sample space contains all the possible outcomes, whether they are favourable or not.

In this question, the event is throwing dice.

The sample space for this event is {1, 2, 3, 4, 5, 6}

For our question, the favourable outcome is getting a prime number.

So, prime numbers: {2, 3, 5}

We can see from the above steps that the number of favourable outcomes where we get a prime number is 3 and the total number of possible outcomes i.e. the number of elements in the sample space is 6.

So, the probability of getting a prime number is:

$P\left( prime
\right)=\dfrac{no.of prime numbers}{total number of outcomes}=\dfrac{3}{6}=\dfrac{1}{2}$
Hence, the probability of getting a prime number is $\dfrac{1}{2}$.
This is our final answer.

Note: In this question, it is very important to know the concept and the formula of probability. The formula for probability of an event is the number of favourable outcomes divided by the total number of possible outcomes. The set of the total number of possible outcomes is called the sample space. So, the sample space contains all the possible outcomes, whether they are favourable or not.