Problem-Solving and Data AnalysisMediumConditional probability from a two-way table
Problem-Solving and Data Analysis practice question
Year 10 — walks: 35, cycles: 10
Year 11 — walks: 25, cycles: 30
The table shows how 100 students travel to school, by year group. If a student who cycles is chosen at random, what is the probability that the student is in Year 10?
- A. 1/4Correct
- B. 1/10
- C. 10/45
- D. 1/5
Answer: A. 1/4
Restrict to students who cycle: 10 + 30 = 40. Of those, 10 are in Year 10, so 10/40 = 1/4.
Why the other answers are wrong
- B. 1/10
- 1/10 divides 10 by all 100 students, ignoring the condition 'cycles'.
- C. 10/45
- 10/45 divides by the number of Year 10 students — the wrong condition (that is P(cycles | Year 10)).
- D. 1/5
- 1/5 would need 8 of 40 cyclists; the table shows 10.
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