This is a curated, evolving list of real Probability theory interview questions and answers, designed by a former Meta Staff Data Scientist who is still actively interviewing candidates (albeit currently as a Staff ML Scientist). Practicing these questions will help you prepare for Data Scientist and Product Data Scientist roles at FAANG and similar-tier companies.
| Problem | Topics | Difficulty |
|---|---|---|
| Documents edited by AI | Bayes rule, Conditional probability | Easy |
| Trailing by two: should we go for two or three? | Independence, Decision making | Easy |
| ( Login required ) Games between two players | Recursive relationship | Medium |
| ( Login required ) Monty Hall | Bayes rule, Conditional independence, Prior evidence | Medium |
| ( Login required ) Red and blue balls | Counting, Combinations, Repetition, Binomial | Easy |
| ( Login required ) Sum of normally distributed random variables | Normal, PDF, CDF | Medium |
| ( Login required ) Two children I | Prior evidence | Easy |
| ( Login required ) Unfair coin probability | Bayes rule, Conditional probability | Easy |
| ( Subscription required ) Consecutive tails | Permutations, Repetition | Easy |
| ( Subscription required ) Largest number rolled | Counting, Permutations, Repetition | Medium |
| ( Subscription required ) Median probability | Binomial, Uniform, CDF | Medium |
| ( Subscription required ) Number of emails | Poisson distribution | Easy |
| ( Subscription required ) Paths to destination | Counting, Combinations | Easy |
| ( Subscription required ) Repeated rolls until 4 | Geometric distribution | Easy |
| ( Subscription required ) Sample digits 1-10 | Sample from samples, Uniform | Medium |
| ( Subscription required ) Two fair die rolls | Independence, CDF, PMF | Easy |