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‎docs/Interview-Questions/Machine-Learning.md‎

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‎docs/Interview-Questions/Natural-Language-Processing.md‎

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‎docs/Interview-Questions/Probability.md‎

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---
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title: Probability Questions
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description: Home page for the platform for Data Science Interview Questions
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title: Probability Interview Questions
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description: A curated list of probability interview questions for data science and technical interviews
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# hide:
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# Probability Interview Questions
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![Total Questions](https://img.shields.io/badge/Total%20Questions-1-blue?style=flat&labelColor=black&color=blue)
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[TOC]
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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 |
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|-----|-----------------------------------------------------------------------|-----------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------|------------|------------------------------------------|
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| 1 | Basic Probability Concepts: Definitions of Sample Space, Event, Outcome | [Wikipedia: Probability](https://en.wikipedia.org/wiki/Probability) | Google, Amazon, Microsoft | Easy | Fundamental Concepts |
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| 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 |
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| 3 | Bayes’ Theorem: Statement and Application | [Wikipedia: Bayes' Theorem](https://en.wikipedia.org/wiki/Bayes%27_theorem) | Google, Amazon, Microsoft | Medium | Bayesian Inference |
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| 4 | Law of Total Probability | [Wikipedia: Law of Total Probability](https://en.wikipedia.org/wiki/Law_of_total_probability) | Google, Facebook | Medium | Theoretical Probability |
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| 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 |
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| 6 | Probability Distributions: Discrete vs. Continuous | [Wikipedia: Probability Distribution](https://en.wikipedia.org/wiki/Probability_distribution) | Google, Amazon, Microsoft | Easy | Distributions |
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| 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 |
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| 8 | Poisson Distribution: Characteristics and Uses | [Wikipedia: Poisson Distribution](https://en.wikipedia.org/wiki/Poisson_distribution) | Google, Amazon | Medium | Discrete Distributions |
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| 9 | Exponential Distribution: Properties and Applications | [Wikipedia: Exponential Distribution](https://en.wikipedia.org/wiki/Exponential_distribution) | Google, Amazon | Medium | Continuous Distributions |
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| 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 |
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| 11 | Law of Large Numbers | [Wikipedia: Law of Large Numbers](https://en.wikipedia.org/wiki/Law_of_large_numbers) | Google, Amazon | Medium | Statistical Convergence |
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| 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 |
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| 13 | Moment Generating Functions (MGFs) | [Wikipedia: Moment-generating function](https://en.wikipedia.org/wiki/Moment-generating_function) | Amazon, Microsoft | Hard | Random Variables, Advanced Concepts |
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| 14 | Markov Chains: Basics and Applications | [Wikipedia: Markov chain](https://en.wikipedia.org/wiki/Markov_chain) | Google, Amazon, Facebook | Hard | Stochastic Processes |
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| 15 | Introduction to Stochastic Processes | [Wikipedia: Stochastic process](https://en.wikipedia.org/wiki/Stochastic_process) | Google, Microsoft | Hard | Advanced Probability |
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| 16 | Difference Between Independent and Mutually Exclusive Events | [Wikipedia: Independent events](https://en.wikipedia.org/wiki/Independence_(probability_theory)) | Google, Facebook | Easy | Fundamental Concepts |
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| 17 | Geometric Distribution: Concept and Use Cases | [Wikipedia: Geometric distribution](https://en.wikipedia.org/wiki/Geometric_distribution) | Amazon, Microsoft | Medium | Discrete Distributions |
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| 18 | Hypergeometric Distribution: When to Use It | [Wikipedia: Hypergeometric distribution](https://en.wikipedia.org/wiki/Hypergeometric_distribution) | Google, Amazon | Medium | Discrete Distributions |
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| 19 | Confidence Intervals: Definition and Calculation | [Khan Academy: Confidence intervals](https://www.khanacademy.org/math/statistics-probability/confidence-intervals) | Microsoft, Facebook | Medium | Inferential Statistics |
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| 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 |
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| 21 | Chi-Squared Test: Basics and Applications | [Wikipedia: Chi-squared test](https://en.wikipedia.org/wiki/Chi-squared_test) | Amazon, Microsoft | Medium | Inferential Statistics |
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| 22 | Permutations and Combinations | [Khan Academy: Permutations and Combinations](https://www.khanacademy.org/math/statistics-probability/probability-library) | Google, Facebook | Easy | Combinatorics |
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| 23 | The Birthday Problem and Its Implications | [Wikipedia: Birthday problem](https://en.wikipedia.org/wiki/Birthday_problem) | Google, Amazon | Medium | Probability Puzzles |
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| 24 | The Monty Hall Problem | [Wikipedia: Monty Hall problem](https://en.wikipedia.org/wiki/Monty_Hall_problem) | Google, Facebook | Medium | Probability Puzzles, Conditional Probability |
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| 25 | Marginal vs. Conditional Probabilities | [Khan Academy: Conditional Probability](https://www.khanacademy.org/math/statistics-probability/probability-library) | Google, Amazon | Medium | Theoretical Concepts |
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| 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 |
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| 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 |
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| 28 | Cumulative Distribution Function (CDF): Definition and Uses | [Wikipedia: Cumulative distribution function](https://en.wikipedia.org/wiki/Cumulative_distribution_function) | Google, Microsoft | Medium | Distributions |
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| 29 | Determining Independence of Events | [Khan Academy: Independent Events](https://www.khanacademy.org/math/statistics-probability/probability-library) | Google, Amazon | Easy | Fundamental Concepts |
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| 30 | Entropy in Information Theory | [Wikipedia: Entropy (information theory)](https://en.wikipedia.org/wiki/Entropy_(information_theory)) | Google, Facebook | Hard | Information Theory, Probability |
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| 31 | Joint Probability Distributions | [Khan Academy: Joint Probability](https://www.khanacademy.org/math/statistics-probability/probability-library) | Microsoft, Amazon | Medium | Multivariate Distributions |
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| 32 | Conditional Expectation | [Wikipedia: Conditional expectation](https://en.wikipedia.org/wiki/Conditional_expectation) | Google, Facebook | Hard | Advanced Concepts |
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| 33 | Sampling Methods: With and Without Replacement | [Khan Academy: Sampling](https://www.khanacademy.org/math/statistics-probability) | Amazon, Microsoft | Easy | Sampling, Combinatorics |
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| 34 | Risk Modeling Using Probability | [Investopedia: Risk Analysis](https://www.investopedia.com/terms/r/risk-analysis.asp) | Google, Amazon | Medium | Applications, Finance |
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| 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 |
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| 36 | Variance under Linear Transformations | [Wikipedia: Variance](https://en.wikipedia.org/wiki/Variance) | Amazon, Facebook | Hard | Advanced Statistics |
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| 37 | Quantiles: Definition and Interpretation | [Khan Academy: Percentiles](https://www.khanacademy.org/math/statistics-probability) | Google, Amazon | Medium | Descriptive Statistics |
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| 38 | Common Probability Puzzles and Brain Teasers | [Brilliant.org: Probability Puzzles](https://brilliant.org/wiki/probability/) | Google, Facebook | Medium | Puzzles, Recreational Mathematics |
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| 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 |
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| 40 | Advanced Topic: Introduction to Stochastic Calculus | [Wikipedia: Stochastic calculus](https://en.wikipedia.org/wiki/Stochastic_calculus) | Microsoft, Amazon | Hard | Advanced Probability, Finance |
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---
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## Questions asked in Google interview
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- Bayes’ Theorem: Statement and Application
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- Conditional Probability and Independence
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- The Birthday Problem
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- The Monty Hall Problem
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- Normal Distribution and the Central Limit Theorem
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- Law of Large Numbers
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## Questions asked in Facebook interview
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- Conditional Probability and Independence
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- Bayes’ Theorem
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- Chi-Squared Test
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- The Monty Hall Problem
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- Entropy in Information Theory
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## Questions asked in Amazon interview
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- Basic Probability Concepts
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- Bayes’ Theorem
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- Expected Value and Variance
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- Binomial and Poisson Distributions
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- Permutations and Combinations
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- Real-World Applications of Bayes’ Theorem
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## Questions asked in Microsoft interview
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- Bayes’ Theorem
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- Markov Chains
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- Stochastic Processes
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- Central Limit Theorem
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- Variance under Linear Transformations
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## Custom Questions
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## Average score on a dice role of at most 3 times
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### Average score on a dice role of at most 3 times
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!!! question
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Consider a fair 6-sided dice.

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