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---
title: Probability Questions
description: Home page for the platform for Data Science Interview Questions
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title: Probability Interview Questions
description: A curated list of probability interview questions for data science and technical interviews
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# - toc
---

# Probability Interview Questions

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[TOC]

This document provides a curated list of common probability interview questions frequently asked in technical interviews. It covers basic probability concepts, probability distributions, key theorems, and real-world applications. Use the practice links to explore detailed explanations and examples.

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| Sno | Question Title | Practice Links | Companies Asking | Difficulty | Topics |
|-----|-----------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------|------------|------------------------------------------|
| 1 | Basic Probability Concepts: Definitions of Sample Space, Event, Outcome | [Wikipedia: Probability](https://en.wikipedia.org/wiki/Probability) | Google, Amazon, Microsoft | Easy | Fundamental Concepts |
| 2 | Conditional Probability and Independence | [Khan Academy: Conditional Probability](https://www.khanacademy.org/math/statistics-probability/probability-library) | Google, Facebook, Amazon | Medium | Conditional Probability, Independence |
| 3 | Bayes’ Theorem: Statement and Application | [Wikipedia: Bayes' Theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem) | Google, Amazon, Microsoft | Medium | Bayesian Inference |
| 4 | Law of Total Probability | [Wikipedia: Law of Total Probability](https://en.wikipedia.org/wiki/Law_of_total_probability) | Google, Facebook | Medium | Theoretical Probability |
| 5 | Expected Value and Variance | [Khan Academy: Expected Value](https://www.khanacademy.org/math/statistics-probability/probability-library) | Google, Amazon, Facebook | Medium | Random Variables, Moments |
| 6 | Probability Distributions: Discrete vs. Continuous | [Wikipedia: Probability Distribution](https://en.wikipedia.org/wiki/Probability_distribution) | Google, Amazon, Microsoft | Easy | Distributions |
| 7 | Binomial Distribution: Definition and Applications | [Khan Academy: Binomial Distribution](https://www.khanacademy.org/math/statistics-probability/random-variables-stats-library) | Amazon, Facebook | Medium | Discrete Distributions |
| 8 | Poisson Distribution: Characteristics and Uses | [Wikipedia: Poisson Distribution](https://en.wikipedia.org/wiki/Poisson_distribution) | Google, Amazon | Medium | Discrete Distributions |
| 9 | Exponential Distribution: Properties and Applications | [Wikipedia: Exponential Distribution](https://en.wikipedia.org/wiki/Exponential_distribution) | Google, Amazon | Medium | Continuous Distributions |
| 10 | Normal Distribution and the Central Limit Theorem | [Khan Academy: Normal Distribution](https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data) | Google, Microsoft, Facebook | Medium | Continuous Distributions, CLT |
| 11 | Law of Large Numbers | [Wikipedia: Law of Large Numbers](https://en.wikipedia.org/wiki/Law_of_large_numbers) | Google, Amazon | Medium | Statistical Convergence |
| 12 | Covariance and Correlation: Definitions and Differences | [Khan Academy: Covariance and Correlation](https://www.khanacademy.org/math/statistics-probability/describing-relationships-quantitatively) | Google, Facebook | Medium | Statistics, Dependency |
| 13 | Moment Generating Functions (MGFs) | [Wikipedia: Moment-generating function](https://en.wikipedia.org/wiki/Moment-generating_function) | Amazon, Microsoft | Hard | Random Variables, Advanced Concepts |
| 14 | Markov Chains: Basics and Applications | [Wikipedia: Markov chain](https://en.wikipedia.org/wiki/Markov_chain) | Google, Amazon, Facebook | Hard | Stochastic Processes |
| 15 | Introduction to Stochastic Processes | [Wikipedia: Stochastic process](https://en.wikipedia.org/wiki/Stochastic_process) | Google, Microsoft | Hard | Advanced Probability |
| 16 | Difference Between Independent and Mutually Exclusive Events | [Wikipedia: Independent events](https://en.wikipedia.org/wiki/Independence_(probability_theory)) | Google, Facebook | Easy | Fundamental Concepts |
| 17 | Geometric Distribution: Concept and Use Cases | [Wikipedia: Geometric distribution](https://en.wikipedia.org/wiki/Geometric_distribution) | Amazon, Microsoft | Medium | Discrete Distributions |
| 18 | Hypergeometric Distribution: When to Use It | [Wikipedia: Hypergeometric distribution](https://en.wikipedia.org/wiki/Hypergeometric_distribution) | Google, Amazon | Medium | Discrete Distributions |
| 19 | Confidence Intervals: Definition and Calculation | [Khan Academy: Confidence intervals](https://www.khanacademy.org/math/statistics-probability/confidence-intervals) | Microsoft, Facebook | Medium | Inferential Statistics |
| 20 | Hypothesis Testing: p-values, Type I and Type II Errors | [Khan Academy: Hypothesis testing](https://www.khanacademy.org/math/statistics-probability/significance-tests) | Google, Amazon, Facebook | Medium | Inferential Statistics |
| 21 | Chi-Squared Test: Basics and Applications | [Wikipedia: Chi-squared test](https://en.wikipedia.org/wiki/Chi-squared_test) | Amazon, Microsoft | Medium | Inferential Statistics |
| 22 | Permutations and Combinations | [Khan Academy: Permutations and Combinations](https://www.khanacademy.org/math/statistics-probability/probability-library) | Google, Facebook | Easy | Combinatorics |
| 23 | The Birthday Problem and Its Implications | [Wikipedia: Birthday problem](https://en.wikipedia.org/wiki/Birthday_problem) | Google, Amazon | Medium | Probability Puzzles |
| 24 | The Monty Hall Problem | [Wikipedia: Monty Hall problem](https://en.wikipedia.org/wiki/Monty_Hall_problem) | Google, Facebook | Medium | Probability Puzzles, Conditional Probability |
| 25 | Marginal vs. Conditional Probabilities | [Khan Academy: Conditional Probability](https://www.khanacademy.org/math/statistics-probability/probability-library) | Google, Amazon | Medium | Theoretical Concepts |
| 26 | Real-World Application of Bayes’ Theorem | [Towards Data Science: Bayes’ Theorem Applications](https://towardsdatascience.com/bayes-theorem-in-machine-learning-6a8b5e9ad0f3) | Google, Amazon | Medium | Bayesian Inference |
| 27 | Probability Mass Function (PMF) vs. Probability Density Function (PDF) | [Wikipedia: Probability density function](https://en.wikipedia.org/wiki/Probability_density_function) | Amazon, Facebook | Medium | Distributions |
| 28 | Cumulative Distribution Function (CDF): Definition and Uses | [Wikipedia: Cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) | Google, Microsoft | Medium | Distributions |
| 29 | Determining Independence of Events | [Khan Academy: Independent Events](https://www.khanacademy.org/math/statistics-probability/probability-library) | Google, Amazon | Easy | Fundamental Concepts |
| 30 | Entropy in Information Theory | [Wikipedia: Entropy (information theory)](https://en.wikipedia.org/wiki/Entropy_(information_theory)) | Google, Facebook | Hard | Information Theory, Probability |
| 31 | Joint Probability Distributions | [Khan Academy: Joint Probability](https://www.khanacademy.org/math/statistics-probability/probability-library) | Microsoft, Amazon | Medium | Multivariate Distributions |
| 32 | Conditional Expectation | [Wikipedia: Conditional expectation](https://en.wikipedia.org/wiki/Conditional_expectation) | Google, Facebook | Hard | Advanced Concepts |
| 33 | Sampling Methods: With and Without Replacement | [Khan Academy: Sampling](https://www.khanacademy.org/math/statistics-probability) | Amazon, Microsoft | Easy | Sampling, Combinatorics |
| 34 | Risk Modeling Using Probability | [Investopedia: Risk Analysis](https://www.investopedia.com/terms/r/risk-analysis.asp) | Google, Amazon | Medium | Applications, Finance |
| 35 | In-Depth: Central Limit Theorem and Its Importance | [Khan Academy: Central Limit Theorem](https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data) | Google, Microsoft | Medium | Theoretical Concepts, Distributions |
| 36 | Variance under Linear Transformations | [Wikipedia: Variance](https://en.wikipedia.org/wiki/Variance) | Amazon, Facebook | Hard | Advanced Statistics |
| 37 | Quantiles: Definition and Interpretation | [Khan Academy: Percentiles](https://www.khanacademy.org/math/statistics-probability) | Google, Amazon | Medium | Descriptive Statistics |
| 38 | Common Probability Puzzles and Brain Teasers | [Brilliant.org: Probability Puzzles](https://brilliant.org/wiki/probability/) | Google, Facebook | Medium | Puzzles, Recreational Mathematics |
| 39 | Real-World Applications of Probability in Data Science | [Towards Data Science](https://towardsdatascience.com/) *(Search for probability applications in DS)* | Google, Amazon, Facebook | Medium | Applications, Data Science |
| 40 | Advanced Topic: Introduction to Stochastic Calculus | [Wikipedia: Stochastic calculus](https://en.wikipedia.org/wiki/Stochastic_calculus) | Microsoft, Amazon | Hard | Advanced Probability, Finance |

---

## Questions asked in Google interview
- Bayes’ Theorem: Statement and Application
- Conditional Probability and Independence
- The Birthday Problem
- The Monty Hall Problem
- Normal Distribution and the Central Limit Theorem
- Law of Large Numbers

## Questions asked in Facebook interview
- Conditional Probability and Independence
- Bayes’ Theorem
- Chi-Squared Test
- The Monty Hall Problem
- Entropy in Information Theory

## Questions asked in Amazon interview
- Basic Probability Concepts
- Bayes’ Theorem
- Expected Value and Variance
- Binomial and Poisson Distributions
- Permutations and Combinations
- Real-World Applications of Bayes’ Theorem

## Questions asked in Microsoft interview
- Bayes’ Theorem
- Markov Chains
- Stochastic Processes
- Central Limit Theorem
- Variance under Linear Transformations

---



## Custom Questions

## Average score on a dice role of at most 3 times
### Average score on a dice role of at most 3 times
!!! question

Consider a fair 6-sided dice.
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