Question

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

Answer 1

Hint: Consider the set of all possible events when a die is thrown. Count the number of prime numbers that can come up when a die is rolled. Use the fact that probability of any event is the ratio of number of favourable outcomes to total number of possible outcomes.

Complete step-by-step answer:
We have to calculate the probability of getting a prime number when a die is thrown.

We will firstly evaluate all possible outcomes when a die is thrown.

So, the set of all possible outcomes are \[\left\{ 1,2,3,4,5,6 \right\}\]. Thus, the number of possible outcomes are 6.

We will now find the set of prime numbers from the given set.

We know that a prime number is the one which has only two factors, 1 and the number itself.

So, the set of prime numbers are \[\left\{ 2,3,5 \right\}\]. Thus, the number of possible outcomes are 3.

We know that probability of any event is the ratio of number of favourable outcomes to total number of possible outcomes.

Thus, the probability of getting a prime number \[=\dfrac{3}{6}=\dfrac{1}{2}\].

Hence, the probability of getting a prime number is \[\dfrac{1}{2}\].

Note: Probability of any event describes how likely an event is to occur or how likely it is that a proposition is true. The value of probability of any event always lies in the range \[\left[ 0,1 \right]\] where having 0 probability indicates that the event is impossible to happen, while having probability equal to 1 indicates that the event will surely happen. We must remember that the sum of probability of occurrence of some event and probability of non-occurrence of the same event is always 1.