Question

A die is rolled. Find the probability of getting a square number.

Answer 1

Hint:- A die has numbers 1, 2, 3, 4, 5 and 6. And the square numbers are those numbers whose square root is a perfect number.

Complete step-by-step answer:
As we know that when a die is rolled then there are six possible outcomes 1, 2, 3, 4, 5 and 6.
And, if the square root of the number is a perfect number (i.e. integer). Then, the number will be a square number. Or we can say that the square of an integer is a square number.
Like some of the square numbers are 1, 4, 9, 16 and 25 because their square roots are 1, 2, 3, 4 and 5 which are integers.
So, out of the six possible outcomes of a die there are only two square numbers and that were 1 and 4.
Now as we know that the formula to find the probability of a favourable outcome is = \[\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}\]
So, the probability of getting a square number will be = \[\dfrac{{{\text{Number of square outcomes}}}}{{{\text{Total number of outcomes}}}} = \dfrac{2}{6} = \dfrac{1}{3}\]
Hence, the probability of getting a square number when a die is rolled will be \[\dfrac{1}{3}\].

Note:- Whenever we come up with this type of problem then first, we had to find the total number of possible outcomes (like here total possible numbers when die is rolled) and after that we had to find the number of favourable outcomes (like here number of square numbers) and then we can directly apply the probability formula to find the probability of getting a favourable outcome i.e. \[\dfrac{{{\text{Number of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}\].