Technical interview guide

Probability Fundamentals

Events, conditional probability, and Bayes' theorem — the building blocks every statistical method assumes.

Read: 44 min
Practice MCQs: 25
Interview QA: 25
Edition: v6
Editorial status: Reviewed
Relevant for: AI EngineerBusiness Intelligence DeveloperComputational BiologistData AnalystData ScientistMachine Learning EngineerProduct ManagerQuantum Software Engineer

Scope: Standards and library references current as of 2026-09: NIST/SEMATECH e-Handbook, the 2016 ASA statement on p-values, SciPy, statsmodels, and NumPy.

Interview QA

Treat each question like a live interview question: answer out loud first (structure, assumptions, tradeoffs), then open the model answer to spot gaps and rehearse a tighter follow-up.

Curated: 2026-10-05 · Written: 2026-10-05 · Reviewed: 2026-10-03

QA-1

Explain sample space and events and how it changes a production decision.

QA-2

How would you reason about conditional probability in a system you own?

QA-3

Walk through bayes' theorem, including where engineers most often get it wrong.

QA-4

What does the base-rate fallacy in production guarantee, and what does it deliberately leave open?

QA-5

Describe independence and the evidence you would collect before relying on it.

QA-6

What is the difference between mutually exclusive events and independent events, and can two events with non-zero probability be both?

QA-7

How do you distinguish discrete from continuous random variables, and what breaks if you evaluate a PDF like a PMF?

QA-8

Teach expectation and linearity to an engineer who has only seen it as a rule of thumb.

QA-9

How do variance and standard deviation differ mathematically and operationally, how does variance behave under scaling and addition, and why do we prefer standard deviation for reporting?

QA-10

What is the Law of Large Numbers (weak vs. strong), what assumptions are required for it to hold, and how does it differ from the Central Limit Theorem?

QA-11

What would you measure before treating the central limit theorem as settled?

QA-12

How does sampling distributions change if the workload grows by two orders of magnitude?

QA-13

A vendor promises confidence intervals is handled for you. What do you still own?

QA-14

When would you refuse a design because of the interval width and sample size?

QA-15

How would you explain covariance and correlation without using the usual slogan?

QA-16

What failure would you inject to check a team's understanding of correlation and causation?

QA-17

How should on-call treat an alert that names simpson's paradox as the cause?

QA-18

What belongs in a runbook section on survivorship and selection bias, and what does not?

QA-19

How would you review a pull request whose risk is expectation versus percentiles?

QA-20

What trade-off does percentiles do not average force that a junior answer usually skips?

QA-21

How would you brief product on why the birthday problem and collisions delays a ship date?

QA-22

What is the smallest experiment that would change your mind about simulation as a check?

QA-23

How does the Monte Carlo error interact with rollback, and where do people ignore that?

QA-24

What would you ask a candidate who recites the conjunction fallacy in estimation but cannot apply it?

QA-25