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

Option d: A and B are mutually exclusive.. Solution: Condition for Addition Theorem Without Intersection The Addition Theorem of Probability states: P(A B) = P(A) + P(B) - P(A B) For the relation P(A B) = P(A) + P(B) to hold, we must have: P(A B) = 0 By definition, two events are mutually exclusive if they cannot occur at the same time, which means their intersection probability is zero. Hence, Option D is the correct answer.

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.. **Condition for Addition Theorem Without Intersection** The Addition Theorem of Probability states: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ For the relation $P(A \cup B) = P(A) + P(B)$ to hold, we must have: $$P(A \cap B) = 0$$ By definition, two events are mutually exclusive if they cannot occur at the same time, which means their intersection probability is zero. Hence, **Option D** is the correct answer.

ProbabilityMCQMTP Sep 24 Series IIQuestion 3375 of 187

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.

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

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.

Detailed Solution & Explanation

**Condition for Addition Theorem Without Intersection** The Addition Theorem of Probability states:

P(A \cup B) = P(A) + P(B) - P(A \cap B)

For the relation

\displaystyle P(A \cup B) = P(A) + P(B)

to hold, we must have:

P(A \cap B) = 0

By definition, two events are mutually exclusive if they cannot occur at the same time, which means their intersection probability is zero. Hence, **Option D** 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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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