From a deck of 52 cards, 3 cards are drawn at random. What is the probability…
2024
From a deck of 52 cards, 3 cards are drawn at random. What is the probability of getting 1 spade, 1 red queen, and 1 black king?
- A.
1/325
- B.
1/415
- C.
1/425
- D.
1/625
Show answer & explanation
Correct answer: C
Classical probability: for equally likely outcomes, P(event) = (favourable outcomes) / (total outcomes). The number of ways to choose r items from n items, when order does not matter, is the combination C(n, r) = n! / (r! × (n − r)!).
Total ways to draw any 3 cards from the 52-card deck: C(52,3) = (52 × 51 × 50)/(3 × 2 × 1) = 22,100.
Ways to choose exactly 1 spade from the 13 spades: C(13,1) = 13.
Ways to choose exactly 1 red queen from the 2 red queens (queen of hearts and queen of diamonds): C(2,1) = 2.
Ways to choose exactly 1 black king from the 2 black kings (king of spades and king of clubs): C(2,1) = 2.
Favourable outcomes = C(13,1) × C(2,1) × C(2,1) = 13 × 2 × 2 = 52.
Required probability = 52 / 22,100 = 1/425.
Independent check: 425 × 52 = 22,100, confirming 52/22,100 simplifies exactly to 1/425.