Exactly two heads — Probability Aptitude Question
Exactly two heads: Three fair coins are tossed. What is the probability of getting exactly two heads? Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 50 seconds
Question
Three fair coins are tossed. What is the probability of getting exactly two heads?
Options
- 1/8
- 1/4
- 3/8
- 1/2
Show the answer and the worked solution
Correct answer: C. 3/8
Worked solution
- Sample space = 2³ = 8 outcomes.
- Exactly two heads: HHT, HTH, THH → 3 outcomes.
- Probability = 3/8.
Answer: 3/8.
The idea
For small coin problems, list the sample space. 'Exactly two' is C(3,2)/2³ = 3/8; 'at least two' would be 4/8.
Shortcut. Exactly two heads just means choosing which single coin shows tails: 3 choices out of 8 outcomes, 3/8.
Common trap. "1/2" — counting 'at least two heads' (HHT, HTH, THH, HHH = 4/8); 'exactly two' excludes HHH.