Problem-Solving and Data AnalysisHardProbability of neither of two events
Problem-Solving and Data Analysis practice question
At a school, 40% of the students take chemistry, 30% take physics, and 15% take both. If a student is selected at random, what is the probability that the student takes neither chemistry nor physics?
Answer: 0.45 or .45 or 9/20 or 45/100
Students taking at least one of the two: 40% + 30% − 15% = 55% (the 15% who take both were counted twice, so subtract once). Neither: 100% − 55% = 45%, so the probability is 0.45.
Common wrong answers
- If you answered 0.3
- 0.3 subtracts 40% and 30% from 100% without adding back the 15% overlap, which double-counts the students who take both.
- If you answered 0.55
- 0.55 is the probability of taking at least ONE of the subjects. The question asks for neither.
- If you answered 0.15
- 0.15 is the share taking BOTH subjects, not neither.
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