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. 6/864 B. 5/12 C. 1/12 D. 625/864

GATE 2018 · General Aptitude · Probability · hard

Answer: P(more girls than boys in group of 3) = 80/220 = 4/11. This question was excluded (X) from the official GATE 2018 EE scoring.

1. Determine the class composition: Let girls = g. Then boys = g + 2. So 2g + 2 = 12, g = 5. Boys = 7, girls = 5.
2. Count total ways to choose 3 from 12: C(12,3) = 1320 / 6 = 220.
3. Count favorable case (2G, 1B): C(5,2) = 10, C(7,1) = 7. Product = 10 * 7 = 70.
4. Count favorable case (3G, 0B): C(5,3) = 10, C(7,0) = 1. Product = 10 * 1 = 10.
5. Compute probability: P = 80 / 220 = 4/11.