At least two heads in three tosses — Aptitude Question
At least two heads in three tosses: Three fair coins are tossed. What is the probability of getting at least two… Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
Three fair coins are tossed. What is the probability of getting at least two heads?
Options
- 1/4
- 3/8
- 1/2
- 5/8
Show the answer and the worked solution
Correct answer: C. 1/2
Worked solution
- Exactly two heads: HHT, HTH, THH (3). Exactly three: HHH (1).
- Favourable = 4 of 8, probability = 1/2.
Answer: 1/2.
The idea
With a small sample space, list it. By symmetry, 'at least two heads' and 'at least two tails' are equally likely and together cover everything, so each is 1/2.
Shortcut. Count with binomials: C(3,2) + C(3,3) = 3 + 1 = 4 of the 2³ = 8 outcomes, so 1/2.
Common trap. 3/8 — counting exactly two heads only and forgetting HHH, which also has at least two heads.