Question

A box conatins cards numbered 6 to 50. A card is drawn at random from the box. The probability that the drawn card has a number which is a perfect square is [CBSE 2013]

(a) $\frac{1}{45}$
(b) $\frac{2}{15}$
(c) $\frac{4}{45}$
(d) $\frac{1}{9}$

Answer 1

Total number of outcomes = 45.

Out of the given numbers, perfect square numbers are 9, 16, 25, 36 and 49.

Numbers of favourable outcomes = 5.

∴ P(getting a number which is a perfect square) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{favourable}\mathrm{outcomes}}{\mathrm{Number}\mathrm{of}\mathrm{all}\mathrm{possible}\mathrm{outcomes}}$
= $\frac{5}{45}=\frac{1}{9}$

Thus, the probability that the drawn card has a number which is a perfect square is $\frac{1}{9}$.

Hence, the correct answer is option (d).