Old Mission Interview Questions
The real Old Mission quant-interview problems candidates report — probability, expected value and statistics — each with a full worked solution.
Inside the Old Mission interview
Old Mission is a Chicago-based options and ETF market maker. Its interviews are grounded in probability and expected value — the everyday math of pricing a fair bet — with a supporting layer of statistics.
What they test
The clear center of gravity is probability (26 problems) — dice, draws, conditional events, and gambler's-ruin / survival puzzles — fused with an expected-value block (12) where you fair-value a game or wager. Around them sit a statistics strand (5), a small stochastic-process and optimization set (4 each), and a light coding tail (4).
The recurring shapes
Expect to condition on the first event and solve for a fixed point: many of these reduce to a recursion of the form E = 1 + p × E, where p is the chance you have to start over. Once you have the probability, you're usually asked what the bet is worth — the expected value is the sum of each outcome weighted by its probability.
How to approach
Reach for symmetry and linearity of expectation before grinding through cases, and write the recursion explicitly rather than guessing. Sanity-check every answer against small cases and extreme limits (probabilities in [0,1], expectations bounded by the best and worst payoff), and when a question turns into a market, state the price you'd quote and the edge it leaves you.
The mix is approachable — 27 easy and 32 medium with only 9 hard — so it rewards solid fundamentals and clean recursions over exotic tricks.
Old Mission probability questions (26)
- World Series Win Probability and Expected Length
- Last White Kitten with Three Black Remaining
- Ordered Candy Draw: First k Red, Last k Blue
- Probability of Rolling a Sum of 4 Before a Sum of 2
- Probability All Dice Show the Same Value
- Uniform Points on a Semicircle Boundary
- Dropped Cards
- Conditional Probability for Uniform Eating Time
- Probability Two Random Subsets Match
- Posterior Probability of a Double-Headed Coin
- Conditional Probability of a Weekend Party Day
- No Complete Pair from a Shoe Closet
- Posterior Fair Value from Noisy Signal
- Probability the Last Red Ball Is Drawn Early
- Stationary Distribution of a Candy Conveyor Belt Markov Chain
- Joint Normal Conditional Probability
- First Ace at Position 33: Probability of the Next Card
- Bayesian Updating with Sequential Trade Direction
- Posterior Probability of an Unsafe Driver Given an Accident
- Bayesian Posterior with Two Binary Signals
- Fraction of Students With Exactly Two Majors
- Hypergeometric Probability: Energy Names in a Hedge Basket
- Poisson Buy-Sell Imbalance
- Poisson Thinning for Toxic Quote Hits
- Probability of an ETF Up Day
- Matching Colors from Two Urns
Old Mission expected value questions (12)
- Expected Flips for Consecutive Heads
- Defective Cat Plushie
- Expected Time to Consume All Large Donuts
- Standard Deviation of a Sum of Card Draws
- Expected Stopping Time and Sum When Rolling Until a Six
- Gamma-Poisson Mixture Distribution
- Exponential Quote Hit Times Across Venues
- First Fill Time Across Multiple Venues
- Limit Order Fill Probability
- Fair Entry Fee for a Two-Coin Flip Game
- Expected Profit per Widget
- Half-Kelly Betting With Equal Wins and Losses
Old Mission statistics questions (5)
Old Mission stochastic processes questions (4)
Old Mission optimization questions (4)
Old Mission coding questions (4)
Old Mission finance questions (4)
Old Mission combinatorics questions (2)
Old Mission market microstructure questions (2)
Old Mission options pricing questions (2)
Old Mission game theory questions (1)
Old Mission linear algebra questions (1)
Old Mission random variables questions (1)
Old Mission interview FAQ
What kind of questions does Old Mission ask in quant interviews?
Candidates most often report probability, expected value and statistics questions. This page collects 68 of them, 67 stamped with the month they were last reported — each with a full worked solution.
How hard are Old Mission interview questions?
The set spans 27 easy, 32 medium and 9 hard problems. Most sit at medium difficulty — solvable in a few minutes with clean reasoning — with a harder tail that rewards knowing the canonical tricks.
How do I prepare for the Old Mission quant interview?
Work through this set by topic (use the sidebar), starting from your weakest area. 18 problems are free to open with their full solution, so you can judge the quality before anything else. Then walk the full Old Mission interview guide for the round-by-round funnel and the online assessment.
Are these the actual Old Mission interview questions?
They are built from candidate-reported Old Mission questions. We rewrite each prompt for clarity and author the worked solutions ourselves — we don't claim the wording is verbatim, and we never invent questions or recycle generic lists. 67 of 68 carry the month they were last reported.