ProbabilityMCQMTP June 24 Series IIIQuestion 3393 of 187
All Questions

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

Options

AP(A)×P(B)\displaystyle P(A) \times P(B)
BP(A)+P(B)\displaystyle P(A) + P(B)
CP(A)+P(B)−P(A∩B)\displaystyle P(A) + P(B) - P(A \cap B)
DP(A)+P(B)−P(A∪B)\displaystyle P(A) + P(B) - P(A \cup B)
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Correct Answer

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

All Options:

  • AP(A)×P(B)\displaystyle P(A) \times P(B)
  • BP(A)+P(B)\displaystyle P(A) + P(B)
  • CP(A)+P(B)−P(A∩B)\displaystyle P(A) + P(B) - P(A \cap B)
  • DP(A)+P(B)−P(A∪B)\displaystyle P(A) + P(B) - P(A \cup B)

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Detailed Solution & Explanation

**Probability of Occurrence of Two Independent Events** By definition: - Two events A\displaystyle A and B\displaystyle B are independent if and only if the probability that both occur (their intersection) is equal to the product of their individual probabilities: P(A∩B)=P(A)×P(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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