Both children girls — Probability Aptitude Question
Both children girls: A family has two children. What is the probability that both are girls, assuming each child is… Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 45 seconds
Question
A family has two children. What is the probability that both are girls, assuming each child is equally likely to be a boy or a girl?
Options
- 1/4
- 1/3
- 1/2
- 2/3
Show the answer and the worked solution
Correct answer: A. 1/4
Worked solution
- Equally likely outcomes: BB, BG, GB, GG.
- Only GG is favourable, so the probability is 1/4.
Answer: 1/4.
The idea
Order matters when listing the sample space: BG and GB are distinct outcomes, which is why the answer is 1/4 rather than 1/3.
Shortcut. Each child is a girl with probability 1/2 independently, so both are girls with probability 1/2 × 1/2 = 1/4; no list is needed.
Common trap. "1/3" — listing only three cases (two boys, one of each, two girls) as if equally likely; 'one of each' happens two ways, BG and GB.