ProbabilityMCQMTP Jun 24 Series IIQuestion 3371 of 187
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If two letters are taken at random from the word HOME, what is the Probability that none of the letters would be vowels?

Options

A1/6\displaystyle 1/6
B1/2\displaystyle 1/2
C1/3\displaystyle 1/3
D1/4\displaystyle 1/4
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Correct Answer

✅ Option a — 1/6\displaystyle 1/6

All Options:

  • A1/6\displaystyle 1/6
  • B1/2\displaystyle 1/2
  • C1/3\displaystyle 1/3
  • D1/4\displaystyle 1/4

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Detailed Solution & Explanation

**Probability that None of the Selected Letters is a Vowel** Letters in the word HOME: {H,O,M,E}\displaystyle \{H, O, M, E\} - Total letters = 4 - Vowels = {O,E}\displaystyle \{O, E\} (count = 2) - Consonants = {H,M}\displaystyle \{H, M\} (count = 2) Two letters are chosen at random. We want to find the probability that none is a vowel, which means both selected letters must be consonants. **Step 1: Calculate total ways to select 2 letters** Total ways=(42)=4×32=6\text{Total ways} = \binom{4}{2} = \frac{4 \times 3}{2} = 6 **Step 2: Calculate ways to select 2 consonants** Favorable ways=(22)=1\text{Favorable ways} = \binom{2}{2} = 1 **Step 3: Calculate the probability** P=16P = \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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