The following table gives the expected value of follow. distribution | P(X) | -20 | -10 | 30 | 75 | 80 ||---|---|---|---|---|---|| P(X) | 3/20 | 1/5 | 1/2 | 1/10 | 1/20 | Find the Expected value of follow. distribution

Option b: 21.5. Solution: Let's calculate the expected value E(X) = sum xi P(xi) . From the given probability distribution table: - Values of X : -20, -10, 30, 75, 80 - Probabilities P(X) : 3/20, 1/5, 1/2, 1/10, 1/20 E(X) = (-20 × 3/20) + (-10 × 1/5) + (30 × 1/2) + (75 × 1/10) + (80 × 1/20) E(X) = -3 - 2 + 15 + 7.5 + 4 E(X) = 21.5 . Hence, Option B is the correct answer.

ProbabilityMCQMTP May 18Question 2844 of 295

All Questions

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

Options

\displaystyle 20.5

\displaystyle 21.5

\displaystyle 22.8

\displaystyle 24.5

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Correct Answer

✅ Option b — $\displaystyle 21.5$

All Options:

A $\displaystyle 20.5$
B $\displaystyle 21.5$
C $\displaystyle 22.8$
D $\displaystyle 24.5$

Detailed Solution & Explanation

Let's calculate the expected value

\displaystyle E(X) = \sum x_i P(x_i)

. From the given probability distribution table: - Values of

\displaystyle X

\displaystyle -20, -10, 30, 75, 80

- Probabilities

\displaystyle P(X)

\displaystyle \frac{3}{20}, \frac{1}{5}, \frac{1}{2}, \frac{1}{10}, \frac{1}{20}

\displaystyle E(X) = \left(-20 \times \frac{3}{20}\right) + \left(-10 \times \frac{1}{5}\right) + \left(30 \times \frac{1}{2}\right) + \left(75 \times \frac{1}{10}\right) + \left(80 \times \frac{1}{20}\right)

\displaystyle E(X) = -3 - 2 + 15 + 7.5 + 4

\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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