(Q13) 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 is
(a) an ace? (b) a queen?

Answer :

Total number of cards = .

∴ Number of total outcomes in picking up a card at random = .

(i) Number of outcomes favourable to queen = .

∴ Probability of getting the queen =
No. of favourable outcomes to the 'Q'
No. of total outcomes
 =

(ii) When queen is drawn and put aside, remaining cards are four.

∴ Number of total outcomes in drawing a card at random = .

(a) Number of favourable outcomes to ace

∴ Probability of getting an Ace =
No. of favourable outcomes
No. of total outcomes
 =

(b) Number of favourable outcomes to 'Q' = 0 (as it was already drawn and put aside)

∴ Probability that the card is Q =
=

After putting queen aside, selecting the queen from the rest is an impossible event and hence the probability is .