Two good bulbs — Probability Aptitude Question
Two good bulbs: From a box of 10 bulbs of which 3 are defective, two are drawn at random. Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
From a box of 10 bulbs of which 3 are defective, two are drawn at random. What is the probability that both are good?
Options
- 7/15
- 7/10
- 1/15
- 3/5
Show the answer and the worked solution
Correct answer: A. 7/15
Worked solution
- Favourable = C(7,2) = 21.
- Total = C(10,2) = 45.
- Probability = 21/45 = 7/15.
Answer: 7/15.
The idea
Reduce the fraction at the end — 21/45 is 7/15, and papers list the reduced form. Read the question twice: 1/15 is the chance that both are defective, the opposite event.
Shortcut. Draw one at a time and cancel: 7/10 × 6/9 = 7/10 × 2/3 = 14/30 = 7/15.
Common trap. "7/10" — stopping at the first draw's chance of a good bulb; the second must be good too (6/9), which brings it down to 7/15.