UPSC NDA II 2018 Mathematics Solved Paper

Concept:Probability is the ratio of favorable outcomes to total outcomes.When selecting one child from each group, the selections are independent.We multiply probabilities for different groups to get joint probability.Explanation:We need exactly 1 girl and 2 boys from the three groups.This can happen in three mutually exclusive cases.Case 1: Girl from Group I, Boy from Group II, Boy from Group III.Probability = $\frac{3}{4} \times \frac{2}{4} \times \frac{3}{4} = \frac{18}{64}$.Case 2: Boy from Group I, Girl from Group II, Boy from Group III.Probability = $\frac{1}{4} \times \frac{2}{4} \times \frac{3}{4} = \frac{6}{64}$.Case 3: Boy from Group I, Boy from Group II, Girl from Group III.Probability = $\frac{1}{4} \times \frac{2}{4} \times \frac{1}{4} = \frac{2}{64}$.Total probability = $\frac{18}{64} + \frac{6}{64} + \frac{2}{64} = \frac{26}{64} = \frac{13}{32}$.Answer:$\frac{13}{32}$ corresponds to option A.