Problem-Solving and Data AnalysisVery hardProbability from a two-way table with a complement
Problem-Solving and Data Analysis practice question
Bus — late: 24, not late: 56
Car — late: 40, not late: 80
The table shows the results of a survey of 200 commuters about their travel mode and whether they arrived late at least once last week. If a bus commuter from the survey is chosen at random, what is the probability that the commuter was NOT late?
- A. 7/10Correct
- B. 3/10
- C. 3/8
- D. 7/20
Answer: A. 7/10
Restrict to bus commuters: 24 late + 56 not late = 80. Not late: 56/80 = 7/10.
Why the other answers are wrong
- B. 3/10
- 3/10 is the probability a bus commuter WAS late (24/80).
- C. 3/8
- 3/8 divides bus-late (24) by all late commuters (64) — the wrong condition.
- D. 7/20
- 7/20 divides bus-not-late (56) by all not-late commuters (160), the wrong condition.
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