If P(A) = 1/2 , P(B) = 1/3 , P(A B) = 1/4 , then the value of P(A' B') is

Option b: 3/4. Solution: Finding P(A' ∪ B') Given: - P(A) = 1/2 - P(B) = 1/3 - P(A B) = 1/4 Using De Morgan's Laws: A' B' = (A B)' Therefore: P(A' B') = 1 - P(A B) P(A' B') = 1 - 1/4 = 3/4 Hence, Option B is the correct answer.

ProbabilityMCQMTP June 22Question 3388 of 187

All Questions

If $\displaystyle P(A) = \frac{1}{2}$ , $\displaystyle P(B) = \frac{1}{3}$ , $\displaystyle P(A \cap B) = \frac{1}{4}$ , then the value of $\displaystyle P(A' \cup B')$ is

Options

\displaystyle \frac{1}{4}

\displaystyle \frac{3}{4}

\displaystyle \frac{2}{5}

DNone of these

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Correct Answer

✅ Option b — $\displaystyle \frac{3}{4}$

All Options:

A $\displaystyle \frac{1}{4}$
B $\displaystyle \frac{3}{4}$
C $\displaystyle \frac{2}{5}$
DNone of these

Detailed Solution & Explanation

**Finding P(A' ∪ B')** Given: -

\displaystyle P(A) = 1/2

\displaystyle P(B) = 1/3

\displaystyle P(A \cap B) = 1/4

Using De Morgan's Laws:

A' \cup B' = (A \cap B)'

Therefore:

P(A' \cup B') = 1 - P(A \cap B)

P(A' \cup B') = 1 - \frac{1}{4} = \frac{3}{4}

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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If P(A)=12\displaystyle P(A) = \frac{1}{2}P(A)=21​, P(B)=13\displaystyle P(B) = \frac{1}{3}P(B)=31​, P(A∩B)=14\displaystyle P(A \cap B) = \frac{1}{4}P(A∩B)=41​, then the value of P(A′∪B′)\displaystyle P(A' \cup B')P(A′∪B′) is