Problem-Solving and Data AnalysisVery hardTwo committee members both from one group
Problem-Solving and Data Analysis practice question
A school council has 4 teachers and 6 parents. Two members are selected at random to form a committee, and no member can be selected twice. What is the probability that both selected members are teachers?
Answer: 2/15
The first selection is a teacher with probability 4/10; then 3 teachers remain among 9 members, so 3/9. (4/10)(3/9) = 12/90 = 2/15.
Common wrong answers
- If you answered 4/25
- 4/25 is (4/10)², which would allow the same person to be chosen twice.
- If you answered 2/5
- 2/5 is the chance that one selection is a teacher, not both.
- If you answered 1/5
- 1/5 adds the probabilities in the wrong way.
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