ProbabilityMCQMTP May 19 Series IIQuestion 3350 of 187

Addition Theorem of Probability states that for any two events $\displaystyle A$ and $\displaystyle B$

Options

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

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

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

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

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Correct Answer

✅ Option c — $\displaystyle P(A \cup B) = P(A) + P(B) - P(A \cap B)$

All Options:

A $\displaystyle P(A \cup B) = P(A) + P(B)$
B $\displaystyle P(A \cup B) = P(A) + P(B) + P(A \cap B)$
C $\displaystyle P(A \cup B) = P(A) + P(B) - P(A \cap B)$
D $\displaystyle P(A \cup B) = P(A) P(B)$

Detailed Solution & Explanation

**Addition Theorem of Probability** The Addition Theorem of Probability for any two events

\displaystyle A

and

\displaystyle B

states that the probability of the union of the two events is given by the sum of their individual probabilities minus the probability of their intersection:

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

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.

Key Concepts to Understand

Probability

A numerical measure of the likelihood of an event occurring, expressed as a number between 0 (impossible) and 1 (certain). Formula: P(A) = Number of favorable outcomes / Total number of equally likely outcomes.

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Addition Theorem of Probability states that for any two events A\displaystyle AA and B\displaystyle BB