A bag contains 25 cards, numbered through 1 to 25. A card is drawn at random. What is the probability that the number on the card drawn is :

(a) a multiple of 5

(b) a perfect square

(c) a prime number ?

Total number of outcomes = 25

(a) Number of multiples of 5 between 1 to 25 = 5 (5, 10, 15, 20, 25).

P(that number on card is a multiples of 5)

= $\dfrac{\text{No. of multiples of 5}}{\text{Total number of outcomes}} = \dfrac{5}{25} = \dfrac{1}{5}$.

Hence, the required probability is $\dfrac{1}{5}$.

(b) Number of perfect squares between 1 to 25 = 5 (1, 4, 9, 16, 25).

P(that number on card is a perfect square)

= $\dfrac{\text{No. of perfect squares}}{\text{Total number of outcomes}} = \dfrac{5}{25} = \dfrac{1}{5}$.

Hence, the required probability is $\dfrac{1}{5}$.

(c) Number of prime numbers between 1 to 25 = 9 (2, 3, 5, 7, 11, 13, 17, 19, 23).

P(that number is a prime number)

= $\dfrac{\text{No. of prime numbers}}{\text{Total number of outcomes}} = \dfrac{9}{25}$.

Hence, the required probability is $\dfrac{9}{25}$.