GATE EE 2018 Set 1 — Question 8
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General Aptitude → Quantitative Aptitude → Elementary Statistics & Probability
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Question
A class of twelve children has two more boys than girls. A group of three children are randomly picked from this class to accompany the teacher on a field trip. What is the probability that the group accompanying the teacher contains more girls than boys?
- A.0
- B.
- C.
- D.
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Solution
Step 1 — Composition of the classLet be the number of girls and the number of boys.Step 2 — Total ways of picking 3 childrenThe three children are picked from the class of 12, so the selection is without replacement:Step 3 — Favourable cases (more girls than boys)In a group of 3 this means either 2 girls and 1 boy, or 3 girls:Step 4 — ProbabilityStep 5 — Comparison with the choicesNone of the four choices equals . The value would arise only if the three picks were treated as independent trials with a fixed probability of a girl each time, i.e. sampling with replacement, which contradicts picking a group of three distinct children from the class. Hence no listed option is correct and full marks are awarded to every candidate.Answer: Marks to all (the correct probability is , which is not among the options).
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