ProbabilityMCQMTP Apr 21Question 3355 of 187

$\displaystyle P(A) = 0.45$ , $\displaystyle P(B) = 0.36$ and $\displaystyle P(A \cap B) = 0.25$ then $\displaystyle P(A/B)$ = ?

Options

\displaystyle 1.40

\displaystyle 1.80

\displaystyle 0.6944

\displaystyle 0.556

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Correct Answer

✅ Option c — $\displaystyle 0.6944$

All Options:

A $\displaystyle 1.40$
B $\displaystyle 1.80$
C $\displaystyle 0.6944$
D $\displaystyle 0.556$

Detailed Solution & Explanation

**Finding P(A/B)** Given: -

\displaystyle P(A) = 0.45

\displaystyle P(B) = 0.36

\displaystyle P(A \cap B) = 0.25

Using the definition of conditional probability:

P(A/B) = \frac{P(A \cap B)}{P(B)}

P(A/B) = \frac{0.25}{0.36} = \frac{25}{36} \approx 0.6944

Hence, **Option C** 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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P(A)=0.45\displaystyle P(A) = 0.45P(A)=0.45, P(B)=0.36\displaystyle P(B) = 0.36P(B)=0.36 and P(A∩B)=0.25\displaystyle P(A \cap B) = 0.25P(A∩B)=0.25 then P(A/B)\displaystyle P(A/B)P(A/B) = ?