Problem-Solving and Data AnalysisMediumProbability of neither of two overlapping events
Problem-Solving and Data Analysis practice question
In a class of 40 students, 25 play a sport, 18 play a musical instrument, and 8 do both. If a student is chosen at random, what is the probability that the student does neither?
Answer: 1/8 or 0.125
Sport or instrument: 25 + 18 − 8 = 35 students. Neither: 40 − 35 = 5. Probability 5/40 = 1/8.
Common wrong answers
- If you answered 23/40
- 23/40 comes from 40 − 25 + 8, ignoring the instrument players entirely.
- If you answered 1/5
- 1/5 is the probability of doing both (8/40).
- If you answered 7/8
- 7/8 is the probability of doing at least one.
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