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
(a) $\frac{1}{45}$
(b) $\frac{2}{15}$
(c) $\frac{4}{45}$
(d) $\frac{1}{9}$
Solution:
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.
$\therefore \mathrm{P}$ (getting a number which is a perfect square) $=\frac{\text { Number of favourable outcomes }}{\text { Number of all possible outcomes }}$
$=\frac{5}{45}=\frac{1}{9}$
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).