ProbabilityMCQMTP June 24 Series IQuestion 2835 of 295

The theory of compound probability states that for any two events A and B:

Options

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

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

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

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

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Correct Answer

✅ Option b — $\displaystyle P(A \cap B) = P(A) \times P(B/A)$

All Options:

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

Detailed Solution & Explanation

The theory of compound probability (also known as the multiplication theorem of probability) states that the probability of the simultaneous occurrence of two events

\displaystyle A

and

\displaystyle B

(i.e., their intersection

\displaystyle P(A \cap B)

) is given by the product of the probability of one event and the conditional probability of the second event given that the first event has occurred. Formally:

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

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

. Let's review the options: - Option A is only true if

\displaystyle A

and

\displaystyle B

are independent. - Option B represents the general statement of compound probability. - Option C is mathematically incorrect. - Option D is the addition theorem of probability, not compound probability. Hence, **Option B** 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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