A card is drawn at random from a well-shuffled pack of 52 playing cards.
Match List-I with List-II
| List-I | List-II | ||
| (A) | Probability that the card is red | (I) | \(\displaystyle\frac{3}{13}\) |
| (B) | Probability that the card is a face card | (II) | \(\displaystyle\frac{3}{52}\) |
| (C) | Probability that the card is an ace | (III) | \(\displaystyle\frac{1}{13}\) |
| (D) | Probability that the card is a face card of spades | (IV) | \(\displaystyle\frac{1}{2}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
The pack has 52 equally likely cards: 26 red and 26 black, in 4 suits of 13 cards each. The face cards are the jack, queen and king of each suit.
(A) Probability that the card is red
This matches (IV) \(\frac{1}{2}\).
\( \displaystyle P = \frac{26}{52} = \frac{1}{2} \)
(B) Probability that the card is a face card
This matches (I) \(\frac{3}{13}\).
There are \(3 \times 4 = 12\) face cards:
\( \displaystyle P = \frac{12}{52} = \frac{3}{13} \)
(C) Probability that the card is an ace
This matches (III) \(\frac{1}{13}\).
\( \displaystyle P = \frac{4}{52} = \frac{1}{13} \)
(D) Probability that the card is a face card of spades
This matches (II) \(\frac{3}{52}\).
Spades have 3 face cards (jack, queen, king):
\( \displaystyle P = \frac{3}{52} \)