ProbabilityMCQPYQ June 24Question 2842 of 295
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A random variable has the following probability distribution: | X | P ||---|---|| 2 | K\displaystyle K || 3 | 2K\displaystyle 2K || 5 | 2K\displaystyle 2K | Find K\displaystyle K.

Options

A1/3\displaystyle 1/3
B2/5\displaystyle 2/5
C1/5\displaystyle 1/5
D2/3\displaystyle 2/3
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Correct Answer

✅ Option c — 1/5\displaystyle 1/5

All Options:

  • A1/3\displaystyle 1/3
  • B2/5\displaystyle 2/5
  • C1/5\displaystyle 1/5
  • D2/3\displaystyle 2/3

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Detailed Solution & Explanation

For any valid probability distribution of a discrete random variable X\displaystyle X, the sum of all probabilities must equal 1: ∑P(X)=1\displaystyle \sum P(X) = 1. Given the distribution: P(X=2)=K\displaystyle P(X=2) = K P(X=3)=2K\displaystyle P(X=3) = 2K P(X=5)=2K\displaystyle P(X=5) = 2K Sum of probabilities: K+2K+2K=1  ⟹  5K=1\displaystyle K + 2K + 2K = 1 \implies 5K = 1. Solving for K\displaystyle K: K=15\displaystyle K = \frac{1}{5}. 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.

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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