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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Correct answer
(MARKS TO ALL)
Solution
1.Determine the number of boys () and girls ():
Total children = 12Given: and .
Substituting in the first equation: .
Then, .
2.Calculate the total number of ways to pick 3 children from 12:
Since the children are picked from a finite class, this is sampling without replacement.Total ways = .
3.Identify the favorable outcomes (more girls than boys):
In a group of 3, 'more girls than boys' occurs in two cases:- Case 1: 3 girls and 0 boys.
- Case 2: 2 girls and 1 boy.
Total favorable ways = .
4.Calculate the probability:
Probability = .5.Conclusion:
None of the given options match the mathematically correct value of . If the problem were incorrectly modeled as sampling with replacement (binomial distribution), the probability would be:.
This matches option (B). However, because the selection is from a finite group without replacement, the question is flawed. Consequently, the official GATE answer key marks this question as Marks to All.
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