For a probability distribution, probability is given by, $P(X_j) = \frac{k}{x_j^2}$, $x_j = 1, 2, \dots, 9$. The value of $k$ is

The correct answer is Option c: $45$. PYQ Dec. 21

ProbabilityPYQ Dec. 21Question 2837 of 276

For a probability distribution, probability is given by, $\displaystyle P(X_j) = \frac{k}{x_j^2}$ , $\displaystyle x_j = 1, 2, \dots, 9$ . The value of $\displaystyle k$ is

Options

\displaystyle 55

\displaystyle 9

\displaystyle 45

\displaystyle 81

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Correct Answer

✅ Option c — $\displaystyle 45$

All Options:

A $\displaystyle 55$
B $\displaystyle 9$
C $\displaystyle 45$
D $\displaystyle 81$

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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For a probability distribution, probability is given by, P(Xj)=kxj2\displaystyle P(X_j) = \frac{k}{x_j^2}P(Xj​)=xj2​k​, xj=1,2,…,9\displaystyle x_j = 1, 2, \dots, 9xj​=1,2,…,9. The value of k\displaystyle kk is