A box has cards numbered 14 to 99. Cards are mixed thoroughly and a card is drawn at random from the box. Find the probability that the card drawn from the box has

(i) an odd number

(ii) a perfect square number.

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

Sample space = {14, 15, 16, ……, 99}, which has 86 equally likely outcomes.

(i) Let A be the event 'odd number', then

A = {15, 17, 19, 21, 23, ………, 91, 93, 95, 97, 99}.

∴ The number of favourable outcomes to the event A = 43.

∴ P(odd number) = $\dfrac{43}{86} = \dfrac{1}{2}.$

Hence, the probability that the number selected is an odd number is $\dfrac{1}{2}.$

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

B = {16, 25, 36, 49, 64, 81}.

∴ The number of favourable outcomes to the event B = 6.

∴ P(a perfect square number) = $\dfrac{6}{86} = \dfrac{3}{43}.$

Hence, the probability that the number selected is a perfect square number is $\dfrac{3}{43}.$