ProbabilityMCQMTP Dec 2023 Series IQuestion 3306 of 187
All Questions

Exactly 3\displaystyle 3 girls are to be selected from 5\displaystyle 5 girls and 3\displaystyle 3 boys. The probability of selecting 3\displaystyle 3 girls will be

Options

A528\displaystyle \frac{5}{28}
B156\displaystyle \frac{1}{56}
C1528\displaystyle \frac{15}{28}
DNone of these
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Correct Answer

✅ Option a — 528\displaystyle \frac{5}{28}

All Options:

  • A528\displaystyle \frac{5}{28}
  • B156\displaystyle \frac{1}{56}
  • C1528\displaystyle \frac{15}{28}
  • DNone of these

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Detailed Solution & Explanation

**Selecting Exactly 3 Girls from 5 Girls and 3 Boys** Total people = 5+3=8\displaystyle 5 + 3 = 8 We need to select a group — the question says 3 girls are selected, implying we choose 3 people from 8 (or from among 5 girls specifically). If selecting 3 from all 8 people: Total ways=(83)=56\text{Total ways} = \binom{8}{3} = 56 Favorable (3 girls)=(53)=10\text{Favorable (3 girls)} = \binom{5}{3} = 10 P=1056=528P = \frac{10}{56} = \frac{5}{28} 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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