ProbabilityMCQPYQ Jun 23Question 3289 of 187
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Four persons are chosen at random from a group of 3 men, 2 women and 4 children. The probability that exactly 2 of them are children is

Options

A1021\displaystyle \frac{10}{21}
B112\displaystyle \frac{1}{12}
C15\displaystyle \frac{1}{5}
D19\displaystyle \frac{1}{9}
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Correct Answer

✅ Option a — 1021\displaystyle \frac{10}{21}

All Options:

  • A1021\displaystyle \frac{10}{21}
  • B112\displaystyle \frac{1}{12}
  • C15\displaystyle \frac{1}{5}
  • D19\displaystyle \frac{1}{9}

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Detailed Solution & Explanation

**4 Persons Chosen: Exactly 2 Children** Group: 3 men + 2 women + 4 children = **9 people total** Total ways to choose 4 from 9: (94)=9!4!⋅5!=9×8×7×64×3×2×1=126\binom{9}{4} = \frac{9!}{4! \cdot 5!} = \frac{9 \times 8 \times 7 \times 6}{4 \times 3 \times 2 \times 1} = 126 Favorable: Exactly 2 children from 4, and 2 others from (3 men + 2 women = 5 adults): (42)×(52)=6×10=60\binom{4}{2} \times \binom{5}{2} = 6 \times 10 = 60 P(exactly 2 children)=60126=1021P(\text{exactly 2 children}) = \frac{60}{126} = \frac{10}{21} Hence, **Option A** is the correct answer.

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

View Official ICAI Syllabus

Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

Key Concepts to Understand

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

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