ProbabilityMCQMTP May 19 Series IIQuestion 2812 of 295

A, B, C are three mutually independent with probabilities $\displaystyle 0.3$ , $\displaystyle 0.2$ and $\displaystyle 0.4$ respectively. What is $\displaystyle P(A \cap B \cap C)$ ?

Options

A0.400

B0.240

C0.024

D0.500

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Correct Answer

✅ Option c — 0.024

All Options:

A0.400
B0.240
C0.024
D0.500

Detailed Solution & Explanation

Given that events

\displaystyle A

\displaystyle B

, and

\displaystyle C

are mutually independent with probabilities: -

\displaystyle P(A) = 0.3

\displaystyle P(B) = 0.2

\displaystyle P(C) = 0.4

For mutually independent events, the probability of their intersection is the product of their individual probabilities:

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

P(A \cap B \cap C) = 0.3 \times 0.2 \times 0.4 = 0.024

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.

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A, B, C are three mutually independent with probabilities 0.3\displaystyle 0.30.3, 0.2\displaystyle 0.20.2 and 0.4\displaystyle 0.40.4 respectively. What is P(A∩B∩C)\displaystyle P(A \cap B \cap C)P(A∩B∩C)?