A multiple of 3 or 5 — Probability Aptitude Question
A multiple of 3 or 5: Tickets numbered 1 to 20 are mixed and one is drawn. What is the probability that it is a… Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
Tickets numbered 1 to 20 are mixed and one is drawn. What is the probability that it is a multiple of 3 or 5?
Options
- 1/2
- 8/15
- 9/20
- 2/5
Show the answer and the worked solution
Correct answer: C. 9/20
Worked solution
- Multiples of 3: 3, 6, 9, 12, 15, 18 → 6 numbers.
- Multiples of 5: 5, 10, 15, 20 → 4 numbers.
- 15 belongs to both, so favourable = 6 + 4 − 1 = 9.
- Probability = 9/20.
Answer: 9/20.
The idea
Inclusion and exclusion: add the two counts and subtract the multiples of the LCM. Missing the overlap gives 10/20 = 1/2.
Shortcut. ⌊20/3⌋ + ⌊20/5⌋ − ⌊20/15⌋ = 6 + 4 − 1 = 9, so 9/20; the only number up to 20 counted twice is 15.
Common trap. "1/2" — adding 6 multiples of 3 and 4 multiples of 5 to get 10/20 without noticing that 15 was counted in both.