Two balls of the same colour — Probability Aptitude Question
Two balls of the same colour: A bag holds 3 red and 5 blue balls. Two are drawn at random. Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 90 seconds
Question
A bag holds 3 red and 5 blue balls. Two are drawn at random. What is the probability that both are the same colour?
Options
- 3/28
- 5/14
- 13/28
- 15/28
Show the answer and the worked solution
Correct answer: C. 13/28
Worked solution
- Both red: C(3,2) = 3. Both blue: C(5,2) = 10.
- Favourable = 13; total = C(8,2) = 28.
- Probability = 13/28.
Answer: 13/28.
The idea
'Same colour' means adding the disjoint cases. The complement, one of each, is 15/28, and the two sum to 1. ✓
Shortcut. Ordered draws: (3 × 2 + 5 × 4) ÷ (8 × 7) = 26/56 = 13/28.
Common trap. "15/28" — counting the 3 × 5 = 15 mixed pairs, the complement, instead of the pairs of one colour.