ProbabilityMCQMTP May 19 Series IIQuestion 2822 of 295

If for two events A and B, $\displaystyle P(A \cap B) = P(A) \times P(B)$ , then the two events A and B are

Options

AIndependent

BDependent

CNot equally likely

DNot exhaustive

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Correct Answer

✅ Option a — Independent

All Options:

AIndependent
BDependent
CNot equally likely
DNot exhaustive

Detailed Solution & Explanation

By mathematical definition, two events

\displaystyle A

and

\displaystyle B

are defined as independent if and only if the joint probability of their occurrence is equal to the product of their individual probabilities:

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

This condition ensures that the probability of occurrence of one event does not affect the probability of occurrence of the other. 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 for two events A and B, P(A∩B)=P(A)×P(B)\displaystyle P(A \cap B) = P(A) \times P(B)P(A∩B)=P(A)×P(B), then the two events A and B are