Quant Interview Probability Cheat Sheet
A compact probability cheat sheet for quant interviews, covering sample spaces, complements, conditioning, Bayes, linearity, and recursion.
Candidates reviewing probability methods before mixed quant interview practice.
Start with the sample space
Before using any formula, define the outcomes. Ask whether order matters, whether items are replaced, whether events are independent, and what information has been revealed. Most probability interview mistakes are denominator mistakes disguised as arithmetic.
Use complements for at-least-one events
When a prompt says at least one, maximum, minimum, or collision, the complement is often smaller. Count the clean failure case and subtract from one. This is the difference between a one-line solution and a long enumeration.
Condition deliberately
Conditional probability changes the universe you are counting inside. Bayes questions are easiest when converted into counts or a two-by-two table. Say both directions out loud: P(signal given state) is not P(state given signal).
Concrete example
For four die rolls, the chance of at least one six is 1 - (5/6)^4. The sample space is four independent ordered rolls. The complement is no sixes, which has probability (5/6)^4. The answer should be above 1/6 and below one.
Remember linearity and recursion
Linearity of expectation helps when a problem asks for an expected count or sum. Recursion helps when the process stops after a state or pattern. Choose the method from the structure, not from the story attached to the problem.
Common mistakes
Candidates memorize formulas without checking assumptions, treat dependent draws as independent, or forget that conditioning changes the denominator. Use this cheat sheet as a prompt for method choice, not as a substitute for practice.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.