Problem-Solving and Data AnalysisEasy–MediumConditional probability from a two-way table
Problem-Solving and Data Analysis practice question
A survey of 100 students at a school recorded each student's year and whether they have a driver's licence.
Seniors: 24 have a licence, 16 do not (40 seniors in total)
Juniors: 30 have a licence, 30 do not (60 juniors in total)
If a senior is chosen at random, what is the probability that the senior has a driver's licence?
- A. 3/5Correct
- B. 4/9
- C. 6/25
- D. 2/5
Answer: A. 3/5
The condition 'a senior is chosen' restricts attention to the 40 seniors. Of those, 24 have a licence, so the probability is 24/40 = 3/5.
Why the other answers are wrong
- B. 4/9
- 4/9 is 24/54 — the 24 licensed seniors out of ALL 54 licensed students. That answers a different question: the probability a licence-holder is a senior.
- C. 6/25
- 6/25 is 24/100, the fraction of ALL students who are licensed seniors. 'If a senior is chosen' means the denominator is the seniors only, 40.
- D. 2/5
- 2/5 is 16/40, the probability a senior does NOT have a licence. The question asks about having one.
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