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 the card is

(i) divisible by 5

(ii) a number which is a perfect square.

A card is selected at random it means that all outcomes are equally likely.

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

(i) Let A be the event 'the number is divisible by 5', then

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

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

∴ P(divisible by 5) = $\dfrac{10}{48} = \dfrac{5}{24}.$

Hence, the probability that the number selected is divisible by 5 is $\dfrac{5}{24}.$

(ii) Let B be the event 'the number is a perfect square', then

B = {16, 25, 36, 49}.

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

∴ P(perfect square) = $\dfrac{4}{48} = \dfrac{1}{12}.$

Hence, the probability that the number selected is a perfect square is $\dfrac{1}{12}.$