Cards marked with numbers 13, 14, 15, …., 60 are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on card drawn is

(i) divisible by 5

(ii) a perfect square number.

The cards are mixed thoroughly and a card is drawn at random from the box means that all the outcomes are equally likely.

Sample space = {13, 14, 15, …., 60}, which has 48 equally likely outcomes.

(i) Let E₁ be the event of choosing card with number that is divisible by 5.

E₁ = {15, 20, 25, 30, 35, 40, 45, 50, 55, 60}.

∴ The number of favourable outcomes to the event E₁ = 10.

$\therefore P(E$1) = \dfrac{\text{No. of favourable outcomes to } E1}{\text{Total no. of possible outcomes}} = \dfrac{10}{48} = \dfrac{5}{24}.

Hence, the probability of choosing a card with number that is divisible by 5 is $\dfrac{5}{24}$.

(ii) Let E₂ be the event of choosing card with perfect square number.

E₂ = {16, 25, 36, 49}.

∴ The number of favourable outcomes to the event E₂ = 4.

$\therefore P(E$2) = \dfrac{\text{No. of favourable outcomes to } E2}{\text{Total no. of possible outcomes}} = \dfrac{4}{48} = \dfrac{1}{12}.

Hence, the probability of choosing a card with perfect square number is $\dfrac{1}{12}$.