ProbabilityMCQMTP May 18Question 2814 of 295

If two events A and B are independent, the probability that both will occur is given by

Options

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

\displaystyle P(A) + P(B)

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

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

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Correct Answer

✅ Option a — $\displaystyle P(A) \times P(B)$

All Options:

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

Detailed Solution & Explanation

By definition, two events

\displaystyle A

and

\displaystyle B

are independent if the occurrence of one does not affect the probability of the occurrence of the other. Mathematically, if

\displaystyle A

and

\displaystyle B

are independent, the probability that both events will occur (which is the probability of their intersection

\displaystyle P(A \cap B)

) is the product of their individual probabilities:

P(A \text{ and } B) = P(A \cap B) = P(A) \times P(B)

Hence, **Option A** 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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