Exactly three heads — Probability Aptitude Question
Exactly three heads: Four fair coins are tossed. What is the probability of getting exactly three heads? Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
Four fair coins are tossed. What is the probability of getting exactly three heads?
Options
- 1/8
- 1/4
- 3/8
- 1/2
Show the answer and the worked solution
Correct answer: B. 1/4
Worked solution
- Sample space = 2⁴ = 16.
- Exactly three heads: C(4,3) = 4 ways.
- Probability = 4/16 = 1/4.
Answer: 1/4.
The idea
Use C(n,k)/2ⁿ for coin problems. Listing the sample space works for four coins but not for more.
Shortcut. Exactly three heads means exactly one tail, and the tail can sit in any of 4 places out of 16 outcomes: 4/16 = 1/4.
Common trap. "1/8" — multiplying (1/2)³ for the three heads, ignoring the fourth coin's tail and the 4 positions it can take.