Two cards are drawn at random from a pack of 52 cards. What is the probability…
2024
Two cards are drawn at random from a pack of 52 cards. What is the probability that either both are black or both are queen?
- A.
4/26
- B.
55/221
- C.
56/221
- D.
55/220
Attempted by 10 students.
Show answer & explanation
Correct answer: B
Total ways to choose 2 cards: C(52,2) = 1326
Probability both are black = C(26,2)/C(52,2) = 325/1326.
Probability both are queens = C(4,2)/C(52,2) = 6/1326.
Probability both are black and both are queens (i.e., both black queens) = C(2,2)/C(52,2) = 1/1326.
Use the union formula: P(either both black or both queens) = 325/1326 + 6/1326 - 1/1326 = 330/1326 = 55/221.
Answer: 55/221