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:

(i) a multiple of 5

(ii) a perfect square

(iii) a prime number

Given,

Sample space = {1, 2, 3, 4, 5, ….., 25}

Total number of outcomes = 25

(i) Let A be the event of getting a multiple of 5, then

A = {5, 10, 15, 20, 25}

∴ The number of favourable outcomes to the event A = 5

∴ P(A) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{5}{25} = \dfrac{1}{5}$

Hence, the probability of getting a multiple of 5 is $\dfrac{1}{5}$.

(ii) Let B be the event of getting a perfect square, then

B = {1, 4, 9, 16, 25}

∴ The number of favourable outcomes to the event B = 5

∴ P(B) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{5}{25} = \dfrac{1}{5}$

Hence, the probability of getting a perfect square is $\dfrac{1}{5}$.

(iii) Let C be the event of getting a prime number, then

C = {2, 3, 5, 7, 11, 13, 17, 19, 23}

∴ The number of favourable outcomes to the event C = 9

∴ P(C) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \dfrac{9}{25}$

Hence, the probability of getting a prime number is $\dfrac{9}{25}$.