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Previous year question hub

Probability - Statistics Previous Year Questions

Practice Probability - Statistics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

8Papers
8Years
60Questions
1Topics

Probability question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Probability. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 36 60%
Easy 20 33.3%
Hard 4 6.7%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

MCQ 29 48.3%
Numerical Answer Type (NAT) 25 41.7%
MSQ 6 10%

Subject weightage

Top subjects by unique question coverage.

Statistics
60 Qs

Most asked topics

Top topics across the included previous year papers.

Probability
60 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Random Variables, Moments and Transformations
48 Qs
Probability Axioms and Conditioning
11 Qs
Probability Inequalities
1 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

Statistics (ST) 2026
12 Qs
Statistics (ST) 2025
7 Qs
Statistics (ST) 2024
9 Qs
Statistics (ST) 2023
10 Qs
Statistics (ST) 2022
5 Qs
Statistics (ST) 2021
8 Qs
Statistics (ST) 2020
4 Qs
Statistics (ST) 2019
5 Qs

Browse by subtopics

Open a focused page built from the same verified paper data.

Random Variables, Moments and Transformations

Explore previous-paper coverage, trends and focused practice for Random Variables, Moments and Transformations.

48 questions8 papers8 years

Probability Axioms and Conditioning

Explore previous-paper coverage, trends and focused practice for Probability Axioms and Conditioning.

11 questions7 papers7 years

Probability Inequalities

Explore previous-paper coverage, trends and focused practice for Probability Inequalities.

1 questions1 papers1 years

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
Statistics (ST) 2026202612View paper
Statistics (ST) 202520257View paper
Statistics (ST) 202420249View paper
Statistics (ST) 2023202310View paper
Statistics (ST) 202220225View paper
Statistics (ST) 202120218View paper
Statistics (ST) 202020204View paper
Statistics (ST) 201920195View paper

Sample previous year questions

A varied preview from the papers represented in this selection, with every available option.

1
2019 · Statistics · Probability · Probability Axioms and Conditioning
Statistics (ST) 2019
Let \(\{1,2,3,4\}\) represent the outcomes of a random experiment, and \(P(\{1\}) = P(\{2\}) = P(\{3\}) = P(\{4\}) = 1/4\). Suppose that \(A_1 = \{1,2\}, A_2 = \{2,3\}, A_3 = \{3,4\}\), and \(A_4 = \{1,2,3\}\). Then which of the following statements is true?
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2
2020 · Statistics · Probability · Random Variables, Moments and Transformations
Statistics (ST) 2020
The moment generating function of a random variable \(X\) is given by \(M_X(t) = \frac{1}{6} + \frac{1}{3}e^t + \frac{1}{3}e^{2t} + \frac{1}{6}e^{3t}, \quad -\infty < t < \infty\). Then \(P(X \le 2)\) equals
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3
2021 · Statistics · Probability · Probability Inequalities
Statistics (ST) 2021
Let \( X \) be a non-constant positive random variable such that \( E(X) = 9 \). Then which one of the following statements is true?
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4
2022 · Statistics · Probability · Random Variables, Moments and Transformations
Statistics (ST) 2022
Let \(X_i\), \(i = 1, 2, ..., n\), be i.i.d. random variables from a normal distribution with mean 1 and variance 4. Let \(S_n = X_1^2 + X_2^2 + \cdots + X_n^2\). If \(Var(S_n)\) denotes the variance of \(S_n\), then the value of \(\lim_{n \to \infty} \left( \frac{Var(S_n)}{n} - \left( \frac{E(S_n)}{n} \right)^2 \right)\) (in integer) is equal to ______
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5
2023 · Statistics · Probability · Probability Axioms and Conditioning
Statistics (ST) 2023
Consider the probability space \( (\Omega, \mathcal{G}, P) \), where \( \Omega = [0, 2] \) and \( \mathcal{G} = \{\phi, \Omega, [0,1), (1,2]\} \). Let \( X \) and \( Y \) be two functions on \( \Omega \) defined as
\[ X(\omega) = \begin{cases} 1 & \text{if } \omega \in [0,1] \\ 2 & \text{if } \omega \in (1,2] \end{cases} \]
and
\[ Y(\omega) = \begin{cases} 2 & \text{if } \omega \in [0,1.5] \\ 3 & \text{if } \omega \in (1.5,2] \end{cases} \]
Then which one of the following statements is true?
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6
2024 · Statistics · Probability · Random Variables, Moments and Transformations
Statistics (ST) 2024
Let \( X \) be a random variable taking only two values, 1 and 2. Let \( M_X(\cdot) \) be the moment generating function of \( X \). If the expectation of \( X \) is \( \frac{10}{7} \), then the fourth derivative of \( M_X(\cdot) \) evaluated at 0 equals
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