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GATE 2018 EE – Question 8

General Aptitude · Quantitative Aptitude: Probability and Combinatorics · 2 marks · Multiple choice

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?

  1. 0
  2. $\frac{325}{864}$
  3. $\frac{525}{864}$
  4. $\frac5{12}$

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Show answer and explanation

Correct answer: (B) $\frac{325}{864}$

Explanation

There are 7 boys and 5 girls. More girls than boys in a group of three means 2 or 3 girls: $\frac{\binom52\binom71+\binom53}{\binom{12}3}=\frac{70+10}{220}=\frac{4}{11}$. This is not among the options, so the question was awarded to all candidates.