Divisible by 3 or 5 — Probability Aptitude Question
Divisible by 3 or 5: A number is chosen at random from 1 to 30. What is the probability that it is divisible by 3… Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 90 seconds
Question
A number is chosen at random from 1 to 30. What is the probability that it is divisible by 3 or 5?
Options
- 7/15
- 1/2
- 8/15
- 3/5
Show the answer and the worked solution
Correct answer: A. 7/15
Worked solution
- Multiples of 3: 10; of 5: 6; of 15: 2.
- Favourable = 10 + 6 − 2 = 14.
- Probability = 14/30 = 7/15.
Answer: 7/15.
The idea
Inclusion and exclusion: add the two counts and subtract the multiples of the LCM. Missing that step gives 16/30.
Shortcut. The pattern repeats every 15: in 1–15 the qualifiers are 3, 5, 6, 9, 10, 12 and 15 — seven — so the probability is 7/15.
Common trap. "8/15" — adding 10 multiples of 3 and 6 multiples of 5 to get 16/30, counting 15 and 30 twice.