ProbabilityMCQPYQ May 18Question 3271 of 187

Sum of all probabilities mutually exclusive and exhaustive events is equal to

Options

B1/2

C1/4

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Correct Answer

✅ Option d — 1

All Options:

A0
B1/2
C1/4
D1

Detailed Solution & Explanation

**Sum of Probabilities of Mutually Exclusive and Exhaustive Events** If events

\displaystyle E_1, E_2, \dots, E_n

are: - **Mutually exclusive**:

\displaystyle E_i \cap E_j = \emptyset

for

\displaystyle i \neq j

(no two events can occur simultaneously) - **Exhaustive**:

\displaystyle E_1 \cup E_2 \cup \dots \cup E_n = S

(their union is the entire sample space) Then by the axiom of probability and the addition rule for mutually exclusive events:

P(E_1 \cup E_2 \cup \dots \cup E_n) = P(E_1) + P(E_2) + \dots + P(E_n)

Since the events are exhaustive:

P(E_1 \cup E_2 \cup \dots \cup E_n) = P(S) = 1

Therefore:

P(E_1) + P(E_2) + \dots + P(E_n) = 1

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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