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

Option a: 5/12. Solution: Evaluating Probability with Typographical Errors Given: - P(A) = 1/2 - P(B) = 1/3 - P(A B) = 1/4 The question asks for the value of P(A B) , which is already given as 1/4 in the text, but this is not in the options (Option A: 5/12 , Option B: 7/12 , Option C: 1/2 ). This indicates a typographical error. Let's test what was likely intended to be asked: 1. If the union P(A B) was asked: P(A B) = P(A) + P(B) - P(A B) = 1/2 + 1/3 - 1/4 = 6 + 4 - 3/12 = 7/12 This matches Option B. 2. If the complement of the union P(A' B') (neither event occurs) was asked: P(A' B') = 1 - P(A B) = 1 - 7/12 = 5/12 This matches Option A. Since the official answer key lists Option A as correct, the question was meant to ask for P(A' B') (i.e., P(A B) ). Hence, Option A is the correct answer.

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

The correct answer is Option a: $5/12$. **Evaluating Probability with Typographical Errors** Given: - $P(A) = 1/2$ - $P(B) = 1/3$ - $P(A \cap B) = 1/4$ The question asks for the value of $P(A \cap B)$, which is already given as $1/4$ in the text, but this is not in the options (Option A: $5/12$, Option B: $7/12$, Option C: $1/2$). This indicates a typographical error. Let's test what was likely intended to be asked: 1. **If the union $P(A \cup B)$ was asked:** $$P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{1}{2} + \frac{1}{3} - \frac{1}{4} = \frac{6 + 4 - 3}{12} = \frac{7}{12}$$ This matches Option B. 2. **If the complement of the union $P(A' \cap B')$ (neither event occurs) was asked:** $$P(A' \cap B') = 1 - P(A \cup B) = 1 - \frac{7}{12} = \frac{5}{12}$$ This matches Option A. Since the official answer key lists Option A as correct, the question was meant to ask for $P(A' \cap B')$ (i.e., $P(\bar{A} \cap \bar{B})$). Hence, **Option A** is the correct answer.

ProbabilityMCQMTP Jun 24 Series IQuestion 3368 of 187

All Questions

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

Options

\displaystyle 5/12

\displaystyle 7/12

\displaystyle 1/2

DNone of these

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option a — $\displaystyle 5/12$

All Options:

A $\displaystyle 5/12$
B $\displaystyle 7/12$
C $\displaystyle 1/2$
DNone of these

Detailed Solution & Explanation

**Evaluating Probability with Typographical Errors** Given: -

\displaystyle P(A) = 1/2

\displaystyle P(B) = 1/3

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

The question asks for the value of

\displaystyle P(A \cap B)

, which is already given as

\displaystyle 1/4

in the text, but this is not in the options (Option A:

\displaystyle 5/12

, Option B:

\displaystyle 7/12

, Option C:

\displaystyle 1/2

). This indicates a typographical error. Let's test what was likely intended to be asked: 1. **If the union

\displaystyle P(A \cup B)

was asked:**

P(A \cup B) = P(A) + P(B) - P(A \cap B) = \frac{1}{2} + \frac{1}{3} - \frac{1}{4} = \frac{6 + 4 - 3}{12} = \frac{7}{12}

This matches Option B. 2. **If the complement of the union

\displaystyle P(A' \cap B')

(neither event occurs) was asked:**

P(A' \cap B') = 1 - P(A \cup B) = 1 - \frac{7}{12} = \frac{5}{12}

This matches Option A. Since the official answer key lists Option A as correct, the question was meant to ask for

\displaystyle P(A' \cap B')

(i.e.,

\displaystyle P(\bar{A} \cap \bar{B})

). 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.

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​ and 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 \cap B)P(A∩B) is