At least one head — Probability Aptitude Question
At least one head: Three fair coins are tossed. What is the probability of getting at least one head? 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 at least one head?
Options
- 1/8
- 3/8
- 5/8
- 7/8
Show the answer and the worked solution
Correct answer: D. 7/8
Worked solution
- P(no heads) = (1/2)³ = 1/8.
- P(at least one head) = 1 − 1/8 = 7/8.
Answer: 7/8.
The idea
'At least one' is nearly always easiest through the complement. Listing the seven favourable outcomes gives the same result more slowly.
Shortcut. Of the 8 equally likely outcomes only TTT has no head, so 7/8 — and any option below 1/2 is out at sight.
Common trap. "3/8" — reading 'at least one head' as 'exactly one head' (3 of the 8 outcomes).