ProbabilityMCQMTP Nov 18Question 2794 of 295

From a bag containing 10 black and 20 white balls, a ball is drawn at random. What is the probability that is black?

Options

\displaystyle \frac{1}{2}

\displaystyle \frac{1}{3}

\displaystyle 1

\displaystyle 2

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Correct Answer

✅ Option b — $\displaystyle \frac{1}{3}$

All Options:

A $\displaystyle \frac{1}{2}$
B $\displaystyle \frac{1}{3}$
C $\displaystyle 1$
D $\displaystyle 2$

Detailed Solution & Explanation

We are given a bag containing: - Black balls =

\displaystyle 10

- White balls =

\displaystyle 20

- Total balls =

\displaystyle 10 + 20 = 30

When a ball is drawn at random, the probability that it is black is:

P(\text{Black}) = \frac{\text{Number of black balls}}{\text{Total number of balls}} = \frac{10}{30} = \frac{1}{3}

This corresponds to Option B. Hence, **Option B** 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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