Question

Cards with numbers \[2\] to \[101\] are placed in a box. A card is selected at random from the box. Find the probability that the selected card has a number which is a perfect square.
A) $\dfrac{{11}}{{100}}$
B) $\dfrac{1}{{10}}$
C) $\dfrac{7}{{100}}$
D) $\dfrac{9}{{100}}$

Answer 1

Hint: We will start with finding favourable outcomes of perfect squares and we are already given total outcomes, so after putting the values in the probability formula we will get our required answer.

Complete step by step answer:
 We have been given a few cards numbered \[2\] to \[101\] are placed in a box. So, we have in total \[100\] cards.
Now a card is selected at random, we need to find the probability that the card selected has a number which is a perfect square.

So, perfect squares between \[2\] and \[101\]\[ = {\text{ }}\left\{ {4,9,16,25,36,49,64,81,100} \right\}\]
Number of favourable outcomes of perfect squares \[ = {\text{ }}9\]
And, the total outcomes of cards \[ = {\text{ }}100\]
We know that, Probability \[ = \] $\dfrac{{favourable{\text{ }}outcomes}}{{total{\text{ }}outcomes}}$
So, probability of getting a number which is a perfect square $ = \dfrac{9}{{100}}$

Hence, option (D), $\dfrac{9}{{100}}$ is correct.

Note: Students should carefully obtain perfect squares from $2$ to \[101.\] As this is the first step and will be our favourable outcomes of perfect squares, so this should be correct, otherwise the answer can get wrong.