Five cards :- the ten, jack, queen, king and ace of diamonds are well-shuffled with their face downwards. One card is then picked up at random.

(i) What is the probability that the card is the queen ?

(ii) If the queen is drawn and put aside, what is the probability that the second card picked up is (a) an ace ? (b) a queen ?

There are five cards.

∴ No. of possible outcomes = 5.

(i) No. of queens = 1

∴ No. of favourable outcomes = 1

P(getting a queen) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{1}{5}$.

Hence, probability of drawing a queen = $\dfrac{1}{5}$.

(ii) Since, queen is drawn and put aside.

∴ No. of cards left = 5 - 1 = 4

∴ No. of possible outcomes = 4.

(a) No. of ace cards = 1

∴ No. of favourable outcomes = 1

P(getting an ace) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{1}{4}$.

Hence, probability of drawing an ace = $\dfrac{1}{4}$.

(b) No. of queen left = 0

∴ No. of favourable outcomes = 0

P(getting a queen) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{0}{4}$ = 0.

Hence, probability of getting a queen = 0.