ProbabilityMCQMTP June 24 Series IIQuestion 3308 of 187

A letter is taken out at random from the word RANGE and another is taken out from the word PAGE. The probability that they are the same letters is

Options

\displaystyle \frac{1}{20}

\displaystyle \frac{3}{20}

\displaystyle \frac{3}{5}

\displaystyle \frac{1}{4}

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Correct Answer

✅ Option b — $\displaystyle \frac{3}{20}$

All Options:

A $\displaystyle \frac{1}{20}$
B $\displaystyle \frac{3}{20}$
C $\displaystyle \frac{3}{5}$
D $\displaystyle \frac{1}{4}$

Detailed Solution & Explanation

**Same Letter from RANGE and PAGE** Letters in RANGE: R, A, N, G, E → 5 distinct letters Letters in PAGE: P, A, G, E → 4 distinct letters Common letters between RANGE and PAGE: **A, G, E** → 3 common letters Total ways to pick one letter from each word =

\displaystyle 5 \times 4 = 20

Favorable outcomes (same letter): - Both pick A: 1 way from RANGE × 1 way from PAGE = 1 - Both pick G: 1 × 1 = 1 - Both pick E: 1 × 1 = 1 Total favorable = **3**

P(\text{same letter}) = \frac{3}{20}

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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