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?

No. of possible outcomes = 5

(i) Out of cards,

No. of favourable outcomes(for getting a queen) = 1

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

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

(ii) Since, queen is drawn and put aside remaining cards = 4.

(a) No. of ace cards = 1

No. of possible outcomes = 4

No. of favourable outcomes (for drawing an ace) = 1

P(drawing 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 queens left after putting a queen card aside = 0.

No. of possible outcomes = 4

No. of favourable outcomes (for drawing a queen) = 0

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

Hence, probability of drawing a queen = 0.