Cards numbered 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is :

(i) a perfect square number

(ii) divisible by 5

(iii) a prime number less than 20.

Given,

Box contains cards numbered from 11 to 60.

∴ No. of cards present = 50

∴ No. of possible outcomes = 50

(i) Favourable outcomes for getting a perfect square number are {16, 25, 36, 49}.

∴ No. of favourable outcomes = 4

P(drawing a perfect square number)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{4}{50} = \dfrac{2}{25}$.

Hence, probability of drawing a perfect square number = $\dfrac{2}{25}$.

(ii) Favourable outcomes for getting a number divisible by 5 are {15, 20, 25, 30, 35, 40, 45, 50, 55, 60}.

∴ No. of favourable outcomes = 10

P(drawing a number divisible by 5)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{10}{50} = \dfrac{1}{5}$.

Hence, probability of drawing a number divisible by 5 = $\dfrac{1}{5}$.

(iii) Favourable outcomes for getting a prime number less than 20 are {11, 13, 17, 19}.

∴ No. of favourable outcomes = 4

P(drawing a prime number less than 20)

= $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{4}{50} = \dfrac{2}{25}$.

Hence, probability of drawing a prime number less than 20 = $\dfrac{2}{25}$.