ProbabilityMCQMTP June 2023 Series IQuestion 2826 of 295

A class consists of $\displaystyle 10$ boys and $\displaystyle 20$ girls in which half the boys and half the girls have blue eyes. Find the probability that a student chosen random is a boy and has blue eyes.

Options

\displaystyle \frac{1}{6}

\displaystyle \frac{3}{5}

\displaystyle \frac{1}{2}

DNone of these

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Correct Answer

✅ Option a — $\displaystyle \frac{1}{6}$

All Options:

A $\displaystyle \frac{1}{6}$
B $\displaystyle \frac{3}{5}$
C $\displaystyle \frac{1}{2}$
DNone of these

Detailed Solution & Explanation

Let's analyze the composition of the class: 1. **Total number of students** in the class is:

10 \text{ boys} + 20 \text{ girls} = 30 \text{ students}

2. We are given that half the boys have blue eyes. The number of blue-eyed boys is:

\frac{1}{2} \times 10 = 5 \text{ boys}

3. We select one student at random from the class of 30. The probability that the selected student is a boy and has blue eyes is the ratio of blue-eyed boys to the total number of students:

\text{Probability} = \frac{\text{Number of blue-eyed boys}}{\text{Total number of students}} = \frac{5}{30} = \frac{1}{6}

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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A class consists of 10\displaystyle 1010 boys and 20\displaystyle 2020 girls in which half the boys and half the girls have blue eyes. Find the probability that a student chosen random is a boy and has blue eyes.