Optiver Statistics & Math Interview Questions
Master your tech interview with our curated database of real questions from top companies.
Solve probability and expectation problems
Probability and Expectation Practice (Take‑home) Assume all coins and dice are fair unless stated otherwise. Show reasoning and final results. 1) Thre...
Find next terms in sequences
Pattern Recognition: Find the Rule and Next Term You are given 8 number sequences. For each sequence: - Identify a clear rule that generates the terms...
Compute odds under time pressure
Timed Probability: At Least Two Reds in Three Draws You have an urn with r red, b blue, and g green balls. Let N = r + b + g with r, b, g ≥ 0 and N ≥ ...
Plan for timed probability assessment
Timed Probability/Statistics Assessment Strategy (30 Questions, Strict Time Limit) Prompt You are taking a timed online assessment with 30 probability...
Analyze EV, arbitrage, and bet sizing across games
Betting Games: EV, Variance, Arbitrage, and Sizing Context You will be shown payout tables or odds for three independent games. Your task is to quickl...
Compute permutations with repeated letters
Counting Strings with Repeated Characters Problem Given two nonnegative integers m and n, how many distinct strings can be formed that contain exactly...
Compute expectations, conditionals, odds, and distributions
Fast Probability and Statistics (No Calculator) Context: Answer quickly with mental math and concise reasoning. Show set-up and any helpful shortcuts....
Compute negative-price probability after n steps
Random-Walk Price Crossing Probability Setup - Initial price: S₀ = s (real number). - Step size: x > 0. - Number of days: n (integer ≥ 0). - Each day ...
Solve numeric sequence pattern puzzles
Sequence Prediction Task You are given five independent number sequences. For each, determine the next term and briefly explain the rule you used. Ass...
Solve quick probability questions
Rapid-Fire Probability Questions Context Answer the following independent probability questions. Assume fair dice/coin and a standard 52-card deck. Sh...
Design dice betting strategy under time limit
Repeated Dice Betting with Time and Risk Constraints You have T = 10 minutes and an initial bankroll B = $1,000 to play a repeated betting game with a...
Optimize interval-scoring strategy
Five-Round Interval-Estimation Game: Optimal Intervals and Risk Allocation You play five independent rounds. In round i, an unknown numeric answer A i...
Compute expected counters after color elimination
Problem You have a bag with 30 counters: 10 red, 10 yellow, and 10 blue. You draw counters uniformly at random without replacement. Stop the moment th...
Compute expected coin flips to meet on octagon
Meeting Time on a Random Walk Around an Octagon Problem Two independent particles start at opposite vertices (four edges apart) of a regular octagon. ...