If y ≥ x , then mathematical expectation is

Option b: E(X) ≤ E(Y). Solution: Finding P(B) for Independent Events Given: - Events A and B are independent. - P(A B) = 0.6 - P(A) = 0.4 Since A and B are independent: P(A B) = P(A) × P(B) = 0.4 P(B) Using the Addition Theorem of Probability: P(A B) = P(A) + P(B) - P(A B) 0.6 = 0.4 + P(B) - 0.4 P(B) 0.2 = 0.6 P(B) P(B) = 0.2/0.6 = 1/3 ≈ 0.333 Hence, Option B is the correct answer.

ProbabilityMCQPYQ June 19Question 3397 of 187

All Questions

If $\displaystyle y \ge x$ , then mathematical expectation is

Options

\displaystyle E(X) \ge E(Y)

\displaystyle E(X) \le E(Y)

\displaystyle E(X) = E(Y)

\displaystyle E(X), E(Y) = 1

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Correct Answer

✅ Option b — $\displaystyle E(X) \le E(Y)$

All Options:

A $\displaystyle E(X) \ge E(Y)$
B $\displaystyle E(X) \le E(Y)$
C $\displaystyle E(X) = E(Y)$
D $\displaystyle E(X), E(Y) = 1$

Detailed Solution & Explanation

**Finding P(B) for Independent Events** Given: - Events

\displaystyle A

and

\displaystyle B

are independent. -

\displaystyle P(A \cup B) = 0.6

\displaystyle P(A) = 0.4

Since

\displaystyle A

and

\displaystyle B

are independent:

P(A \cap B) = P(A) \times P(B) = 0.4 P(B)

Using the Addition Theorem of Probability:

P(A \cup B) = P(A) + P(B) - P(A \cap B)

0.6 = 0.4 + P(B) - 0.4 P(B)

0.2 = 0.6 P(B)

P(B) = \frac{0.2}{0.6} = \frac{1}{3} \approx 0.333

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.

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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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If y≥x\displaystyle y \ge xy≥x, then mathematical expectation is