For two events $A$ and $B$, $P(A \cup B) = P(A) + P(B)$ only when

$A$ and $B$ are mutually exclusive.

$A$ and $B$ are equally likely events

$A$ and $B$ are exhaustive events

$A$ and $B$ are mutually independent

$A$ and $B$ are mutually exclusive.

For two events $A$ and $B$, $P(A \cup B) = P(A) + P(B)$ only when

The correct answer is Option d: $A$ and $B$ are mutually exclusive.. MTP Sep 24 Series II

ProbabilityMTP Sep 24 Series IIQuestion 3375 of 170

All Questions

For two events $\displaystyle A$ and $\displaystyle B$ , $\displaystyle P(A \cup B) = P(A) + P(B)$ only when

Options

\displaystyle A

and

\displaystyle B

are equally likely events

\displaystyle A

and

\displaystyle B

are exhaustive events

\displaystyle A

and

\displaystyle B

are mutually independent

\displaystyle A

and

\displaystyle B

are mutually exclusive.

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Correct Answer

✅ Option d — $\displaystyle A$ and $\displaystyle B$ are mutually exclusive.

All Options:

A $\displaystyle A$ and $\displaystyle B$ are equally likely events
B $\displaystyle A$ and $\displaystyle B$ are exhaustive events
C $\displaystyle A$ and $\displaystyle B$ are mutually independent
D $\displaystyle A$ and $\displaystyle B$ are mutually exclusive.

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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For two events A\displaystyle AA and B\displaystyle BB, P(A∪B)=P(A)+P(B)\displaystyle P(A \cup B) = P(A) + P(B)P(A∪B)=P(A)+P(B) only when