Problem-Solving and Data AnalysisVery hardTotal probability across two groups
Problem-Solving and Data Analysis practice question
In a club, 40% of the members are students. Three quarters of the student members and one half of the non-student members have signed up for a trip. If a member is chosen at random, what is the probability that the member has signed up for the trip?
Answer: 3/5 or 0.6
0.4 × 0.75 + 0.6 × 0.5 = 0.3 + 0.3 = 0.6.
Common wrong answers
- If you answered 0.3
- 0.3 counts only the students who signed up.
- If you answered 0.625
- 0.625 averages 3/4 and 1/2, ignoring the group sizes.
- If you answered 0.75
- 0.75 is the sign-up rate among students alone.
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