Problem-Solving and Data AnalysisMediumAt least one girl among two children
Problem-Solving and Data Analysis practice question
A family has two children, each of whom is equally likely to be a boy or a girl, independently. What is the probability that at least one of the children is a girl?
- A. 3/4Correct
- B. 1/2
- C. 1/4
- D. 2/3
Answer: A. 3/4
The only way to have NO girl is boy-boy, with probability (1/2)(1/2) = 1/4. At least one girl is the complement: 1 − 1/4 = 3/4.
Why the other answers are wrong
- B. 1/2
- 1/2 is the probability that one PARTICULAR child is a girl, or that there is exactly one girl.
- C. 1/4
- 1/4 is the probability of no girls (or of two girls).
- D. 2/3
- There are four equally likely outcomes (BB, BG, GB, GG), not three.
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