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The following table gives the expected value of follow. distribution | P(X) | -20 | -10 | 30 | 75 | 80 ||---|---|---|---|---|---|| P(X) | 320\displaystyle \frac{3}{20} | 15\displaystyle \frac{1}{5} | 12\displaystyle \frac{1}{2} | 110\displaystyle \frac{1}{10} | 120\displaystyle \frac{1}{20} | Find the Expected value of follow. distribution

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

✅ Option b — $21.5$

All Options:

  • A$20.5$
  • B$21.5$
  • C$22.8$
  • D$24.5$

Detailed Solution & Explanation

Let's calculate the expected value E(X)=∑xiP(xi)\displaystyle E(X) = ∑\displaystyle \sum x_i P(x_i). From the given probability distribution table: - Values of X\displaystyle X: −20,−10,30,75,80\displaystyle -20, -10, 30, 75, 80 - Probabilities P(X)\displaystyle P(X): 320,15,12,110,120\displaystyle 320\displaystyle \frac{3}{20}, 15\displaystyle \frac{1}{5}, 12\displaystyle \frac{1}{2}, 110\displaystyle \frac{1}{10}, 120\displaystyle \frac{1}{20} E(X)=(−20×320)+(−10×15)+(30×12)+(75×110)+(80×120)\displaystyle E(X) = \left(-20 ×\displaystyle \times 320\displaystyle \frac{3}{20}\right) + \left(-10 ×\displaystyle \times 15\displaystyle \frac{1}{5}\right) + \left(30 ×\displaystyle \times 12\displaystyle \frac{1}{2}\right) + \left(75 ×\displaystyle \times 110\displaystyle \frac{1}{10}\right) + \left(80 ×\displaystyle \times 120\displaystyle \frac{1}{20}\right) E(X)=−3−2+15+7.5+4\displaystyle E(X) = -3 - 2 + 15 + 7.5 + 4 E(X)=21.5\displaystyle E(X) = 21.5. 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.

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