There are 6 men and 7 women in a committee. 2 people need to be selected as…
2023
There are 6 men and 7 women in a committee. 2 people need to be selected as representatives of this committee. What is the probability that out of these two people one is a man and another is a woman?
- A.
3/13
- B.
7/26
- C.
5/26
- D.
7/13
Attempted by 29 students.
Show answer & explanation
Correct answer: D
Key idea: count the total number of 2-person selections and the number of selections with one man and one woman.
Combination method: Total ways to choose 2 from 13 = C(13,2) = 78. Favourable ways (one man and one woman) = 6 × 7 = 42. Probability = 42/78 = 7/13.
Sequential probability method (alternative): Probability of man then woman = (6/13) × (7/12). Probability of woman then man = (7/13) × (6/12). Sum = 2 × (6 × 7) / (13 × 12) = 84/156 = 7/13.
Answer: 7/13