One of each colour — Probability Aptitude Question
One of each colour: A bag has 4 white and 5 black balls. Two are drawn at random. Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
A bag has 4 white and 5 black balls. Two are drawn at random. What is the probability that they are of different colours?
Options
- 5/18
- 4/9
- 5/9
- 2/3
Show the answer and the worked solution
Correct answer: C. 5/9
Worked solution
- Favourable = C(4,1) × C(5,1) = 20.
- Total = C(9,2) = 36.
- Probability = 20/36 = 5/9.
Answer: 5/9.
The idea
One from each group multiplies the two counts. The complement (both the same colour) would be 16/36, confirming the total.
Shortcut. Take one order and double it: white then black is 4/9 × 5/8 = 20/72, and black then white is the same, so 40/72 = 5/9.
Common trap. "5/18" — counting only white-then-black, 4/9 × 5/8 = 5/18; black-then-white is equally likely, so the answer doubles to 5/9.