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 a side, what is the probability that the second card picked up is (a) an ace? (b) a queen?
Answers
(i) The probability that the card drawn is a queen is 1 / 5.
(ii) (a) The probability that the second card picked up is an ace is 1 / 4.
(b) The probability that the second card picked up is a queen is 0.
• The given cards are :
The ten of diamond = 1
The jack of diamond = 1
The queen of diamond = 1
The king of diamond = 1
The ace of diamond = 1
∴ Total number of cards in the pack = 1 + 1 + 1 + 1 + 1 = 5
(i) Probability of drawing the queen from the pack = Number of queens in the pack / Total number of cards in the pack
Or, Probability of drawing the queen = 1 / 5
(ii) (a) Number of cards remaining in the pack after picking up the queen = 5 - 1 = 4
∴Probability that the second card picked up is an ace = Number of aces in the pack / Number of cards remaining in the pack
Or, Probability of picking up an ace = 1 / 4
(b) Number of queens left in the pack = 0
∴ Probability of picking up a queen again = Number of queens left / Remaining number of cards in the pack
Or, probability of drawing a queen = 0 / 4 = 0