A bag contains 8 red and 5 white balls. 2 balls are drawn at random. What is…
2025
A bag contains 8 red and 5 white balls. 2 balls are drawn at random. What is the probability that both are white ?
- A.
3/39
- B.
5/39
- C.
1/39
- D.
4/39
Attempted by 27 students.
Show answer & explanation
Correct answer: B
We want the probability that both drawn balls are white when drawing two balls without replacement from 8 red and 5 white (total 13).
Method 1 — sequential probability:
Probability the first ball is white = 5/13.
Given the first is white, probability the second is white = 4/12.
Multiply: (5/13) × (4/12) = 20/156 = 5/39.
Method 2 — combinatorial approach:
Number of ways to choose 2 white balls = C(5,2) = 10.
Total ways to choose any 2 balls = C(13,2) = 78.
Probability = 10/78 = 5/39.
Final answer: 5/39