ProbabilityMCQPYQ Nov. 19Question 3317 of 187
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Two letters are chosen from the word HOME. What is the probability that the letters chosen are not vowels.

Options

A12\displaystyle \frac{1}{2}
B16\displaystyle \frac{1}{6}
C23\displaystyle \frac{2}{3}
D0\displaystyle 0
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Correct Answer

✅ Option b — 16\displaystyle \frac{1}{6}

All Options:

  • A12\displaystyle \frac{1}{2}
  • B16\displaystyle \frac{1}{6}
  • C23\displaystyle \frac{2}{3}
  • D0\displaystyle 0

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Detailed Solution & Explanation

**Two Letters from HOME — Neither Vowel** Word: HOME → Letters: H, O, M, E - Vowels: O, E → 2 vowels - Consonants: H, M → 2 consonants Total ways to choose 2 letters from 4: (42)=6\binom{4}{2} = 6 Favorable (both not vowels = both consonants): (22)=1\binom{2}{2} = 1 P(no vowels)=16P(\text{no vowels}) = \frac{1}{6} Note: The given answer is A = 12\displaystyle \frac{1}{2}, but by derivation, P=16\displaystyle P = \frac{1}{6} = Option B. By mathematical derivation, the answer is 16\displaystyle \frac{1}{6}. 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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