Question

A die is thrown then find the probability of getting a perfect square.
A. $\dfrac{1}{3}$
B. $\dfrac{1}{2}$
C. $\dfrac{2}{3}$
D. 0

Answer 1

Hint : A perfect square is an integer which is a square of another integer. When a die is thrown the possible outcomes are 1, 2, 3, 4, 5 and 6. From these outcomes, find the outcomes which are perfect squares and then find the probability of getting those outcomes.

Complete step-by-step answer :
We are given to find the probability of getting a perfect square when a die is thrown.

Probability of an event is the ratio of no. of favorable outcomes to the event and the total no. of outcomes possible.
When a die is thrown, the total no. of outcomes possible are 6, they are 1, 2, 3, 4, 5 and 6. These numbers are shown on the face of the die when it is thrown.
A perfect square is an integer which is a product of another integer with itself.
Out of the outcomes, 1, 2, 3, 4, 5, 6, the outcomes 1 and 4 are perfect squares.
Because 1 is the product of itself and 4 is the product of 2 and 2.
No. of outcomes which are perfect squares is 2.
Probability of getting a perfect square when a die is thrown is $\dfrac{2}{6} = \dfrac{1}{3}$

So, the correct answer is “Option A”.

Note : Total no. of outcomes of an experiment can also be termed as sample space. The sample space of throwing a die is 1, 2, 3, 4, 5 and 6, which means these are the total possible outcomes from doing the experiment. The set of possible outcomes of any event is always a subset of sample space.