Problem-Solving and Data AnalysisHardConditional probability from a two-way table
Problem-Solving and Data Analysis practice question
Age | Owns a bicycle | Does not own a bicycle
Under 30 | 40 | 20
30 or over | 25 | 35
If a person who owns a bicycle is chosen at random from those surveyed, what is the probability that the person is under 30?
- A. 8/13Correct
- B. 2/3
- C. 1/3
- D. 13/24
Answer: A. 8/13
The choice is made from bicycle OWNERS only: 40 + 25 = 65 people. Of those, 40 are under 30: 40/65 = 8/13.
Why the other answers are wrong
- B. 2/3
- 2/3 is 40/60 — the fraction of UNDER-30s who own a bicycle, the reverse condition.
- C. 1/3
- 1/3 is 40/120, dividing by everyone surveyed instead of by the bicycle owners.
- D. 13/24
- 13/24 is 65/120, the probability that a random surveyed person owns a bicycle.
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