ProbabilityMCQPYQ Dec. 21Question 3282 of 187
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Which of the following pair of events E\displaystyle E and F\displaystyle F are mutually exclusive?

Options

AE=(Ram’s age is 13) and F=(Ram is studying in a college)\displaystyle E = (\text{Ram's age is } 13) \text{ and } F = (\text{Ram is studying in a college})
BE=(Sita studies in a school) and F=(Sita is a play back singer)\displaystyle E = (\text{Sita studies in a school}) \text{ and } F = (\text{Sita is a play back singer})
CE=(Raju is an elder brother in a family) and F=(Raju’s father has more than one son)\displaystyle E = (\text{Raju is an elder brother in a family}) \text{ and } F = (\text{Raju's father has more than one son})
DE=(Banu studied B.A. English literature and)F=(Banu can read English novels)\displaystyle E = (\text{Banu studied B.A. English literature and}) F = (\text{Banu can read English novels})
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Correct Answer

✅ Option a — E=(Ram’s age is 13) and F=(Ram is studying in a college)\displaystyle E = (\text{Ram's age is } 13) \text{ and } F = (\text{Ram is studying in a college})

All Options:

  • AE=(Ram’s age is 13) and F=(Ram is studying in a college)\displaystyle E = (\text{Ram's age is } 13) \text{ and } F = (\text{Ram is studying in a college})
  • BE=(Sita studies in a school) and F=(Sita is a play back singer)\displaystyle E = (\text{Sita studies in a school}) \text{ and } F = (\text{Sita is a play back singer})
  • CE=(Raju is an elder brother in a family) and F=(Raju’s father has more than one son)\displaystyle E = (\text{Raju is an elder brother in a family}) \text{ and } F = (\text{Raju's father has more than one son})
  • DE=(Banu studied B.A. English literature and)F=(Banu can read English novels)\displaystyle E = (\text{Banu studied B.A. English literature and}) F = (\text{Banu can read English novels})

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Detailed Solution & Explanation

**Identifying Mutually Exclusive Events** Mutually exclusive events cannot occur simultaneously. Let's analyze each option: **Option A:** E = Ram's age is 13; F = Ram is studying in college. - A 13-year-old typically cannot be in college (college age is generally 17+). - These two events **cannot occur simultaneously**. → **Mutually exclusive** ✓ **Option B:** E = Sita studies in school; F = Sita is a playback singer. - A student in school can also be a playback singer. These **can occur simultaneously**. → Not mutually exclusive. **Option C:** E = Raju is an elder brother; F = Raju's father has more than one son. - If Raju is an elder brother, his father must have at least 2 sons. These **always occur together**. → Not mutually exclusive. **Option D:** E = Banu studied B.A. English; F = Banu can read English novels. - Studying English literature implies ability to read novels. These **occur together**. → Not mutually exclusive. The pair in Option A are mutually exclusive because a 13-year-old cannot simultaneously be a college student. 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.

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