Two red balls — Probability Aptitude Question
Two red balls: A bag contains 5 red and 4 green 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 contains 5 red and 4 green balls. Two are drawn at random. What is the probability that both are red?
Options
- 5/18
- 5/9
- 2/9
- 1/6
Show the answer and the worked solution
Correct answer: A. 5/18
Worked solution
- Ways to choose 2 red = C(5,2) = 10.
- Total ways = C(9,2) = 36.
- Probability = 10/36 = 5/18.
Answer: 5/18.
The idea
Counting combinations avoids worrying about order. Drawing sequentially gives (5/9) × (4/8) = 5/18 as well.
Shortcut. The second draw's 4/8 is exactly 1/2, so the answer is simply half the first draw's 5/9: 5/18.
Common trap. "5/9" — stopping at the first draw's chance of red; both balls must be red, so it is multiplied by 4/8 for the second.