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?

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option a — E=(Ram’s age is 13) and F=(Ram is studying in a college)\displaystyle E = (\displaystyle \text{Ram's age is } 13)  and \displaystyle \text{ and } F = (Ram is studying in a college\displaystyle \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 = (\displaystyle \text{Ram's age is } 13)  and \displaystyle \text{ and } F = (Ram is studying in a college\displaystyle \text{Ram is studying in a college})
  • BE=(Sita studies in a school) and F=(Sita is a play back singer)\displaystyle E = (Sita studies in a school\displaystyle \text{Sita studies in a school})  and \displaystyle \text{ and } F = (Sita is a play back singer\displaystyle \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 = (Raju is an elder brother in a family\displaystyle \text{Raju is an elder brother in a family})  and \displaystyle \text{ and } F = (\displaystyle \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 = (Banu studied B.A. English literature and\displaystyle \text{Banu studied B.A. English literature and}) F = (Banu can read English novels\displaystyle \text{Banu can read English novels})

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.

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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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