Question

A card is drawn from a deck of cards numbered 1 to 52. The probability that the number on the card is a perfect square is
(a) $\dfrac{1}{13}$
(b) $\dfrac{2}{13}$
(c) $\dfrac{7}{52}$
(d) $\dfrac{10}{13}$

Answer 1

Hint: To find the probability of the drawing a card with a perfect square number from a deck of cards, we have to use the formula for probability of an event which is given by
$ P\left( E \right)=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$ . We have to find the number of perfect squares from 1 to 52 and divide it by the total number of cards.

Complete step by step answer:
We have to find the probability of drawing a card with a perfect square number from a deck of cards. We know that probability of an event is the number of favourable outcomes divided by the total number of outcomes.
$\Rightarrow P\left( E \right)=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
We know that perfect squares from 1 to 52 are 1, 4, 9, 16, 25, 36, 49. Therefore, the number of favourable outcomes is 7. Total number of outcomes will be 52 since we are looking for perfect squares from 1 to 52.
$\Rightarrow P\left( \text{perfect square} \right)=\dfrac{7}{52}$

So, the correct answer is “Option c”.

Note: Students must be thorough with the formulas for probability as there is a chance that they may write it as the total number of outcomes divided by the number of favourable outcomes. They must note that the probability of an event will be a value between 0 and 1, that is, \[0\le P\left( E \right)\le 1\] .