Introduction to Probability Questions
Probability theory forms the foundation to use statistical inference methods by providing the mathematical framework essential for understanding and quantifying uncertainty, making informed decisions, and extracting meaningful insights from data. To perform high-quality hypothesis tests and regression analyses, you need a strong understanding of probability theory.
Interviewers are evaluating not only your conceptual knowledge of these concepts, but also your ability to use mathematical notation and code to run simulations.
In this module, we'll review probability concepts and what to expect in interviews.
What to expect
Questions related to probability are usually given in the following formats:
Conceptual questions
- Why is the sample size important when considering the applicability of the Central Limit Theorem?
- Explain Bayes Theorem.
Numerical questions
- A $5 discount coupon is given to N riders. The probability of using a coupon is P. What is the expected cost for the company?
- What's the probability of obtaining 2 tails in 5 coin flips?
Applied questions
- Suppose you're working for a healthcare organization that wants to estimate the average recovery time for patients undergoing a specific medical procedure. How would you leverage the Law of Large Numbers to ensure the reliability of your estimation?
How to prepare
To brush up on probability-related questions:
- Review key probability concepts, assumptions, and mathematical formulas.
- Work through practice problems and datasets, with a focus on solving problems that apply probability concepts to real-world scenarios, such as gambling games.
- If you have the time, study math textbooks (e.g. Introduction to Probability) that teach probability theory and its applications.
- Practice using statistical software like R or Python to code formulas and run simulations. Learn how to formulate and model probabilistic problems using mathematical notation and logical reasoning.