PRACTICE GUIDE CITADEL SECURITIES
Citadel Securities Probability OA Practice Test
The Citadel Securities probability oa screen is 15 questions in 30 minutes - about 2 minutes each - answered by typing the number, with no calculator. There is no negative marking, so leaving an item blank gains you nothing over guessing.
Where it sits: Second part of a two-test online round. The practice sitting on this page runs the same item count, the same clock and the same marking rule, with questions generated by Outcry rather than taken from Citadel Securities.
Outcry is not affiliated with Citadel Securities and has no access to their assessment content. This guide describes an assessment format that candidates report publicly; the questions here are generated by Outcry and are not Citadel Securities’s own.
What it screens
A market maker quoting across equities, options, fixed income and ETFs globally.
- ✓Expected value computed fast and used to make a decision
- ✓Conditional probability and Bayes updates without formal notation
- ✓Ranking likelihoods rather than computing them exactly
- ✓Fermi estimation: decomposing an impossible question into three easy ones
Where it sits at Citadel Securities
This section does not arrive on its own. It closes the paper, and the sitting around it runs 42 minutes and 65 items in total, with Cognitive screen on the same continuous clock. Candidates who prepare only for this round tend to be caught by the pacing of the rest.
There is no going back. You answer or skip, and the next item loads, which means the decision to leave an item is final at the moment you make it.
The format
These are the numbers the Citadel Securities sitting on this site runs on, matching the format candidates report.
| Questions | 15 |
|---|---|
| Time | 30 minutes |
| Per question | 2 minutes |
| Negative marking | No |
| Answer style | Typed numeric answer, no calculator |
| Where it sits | Second part of a two-test online round |
What it tests, with a worked example
Every example below is generated by Outcry, drawn from the same question generators the timed drills run. None of them is Citadel Securities’s.
Expected value and odds
Pricing a bet, converting between odds and probabilities, and deciding whether to take it.
Example
You win 20 with probability 65% and lose 20 otherwise. Expected value per bet?
- 6
- 13
- 20
- 0
Answer 6
65% × 20 − 35% × 20 = 6. The edge is the probability gap times the stake.
Distributions you should know cold
Binomial, geometric and uniform means and variances, applied rather than quoted.
Example
Two fair dice are rolled. What is the chance the total is 8?
- 13.9%
- 41.7%
- 16.7%
- 23.8%
- 9.1%
Answer 13.9%
5 of the 36 ordered pairs total 8, so 5/36 = 13.9%. There are 11 totals and 21 unordered pairs, and neither set is equally likely.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
Stock Price FOXTROT $192.99 CEDAR $275.93 INDIGO $229.45 GAMMA $78.63 ALFA $177.05
The index above is price weighted with a divisor of 4.7703. GAMMA at $78.63 is replaced by ECHO at $243.00. What is the new divisor?
Answer 5.5922
The index level cannot jump on a corporate action, because nobody's wealth changed. Before: the prices sum to $954.05 and the level is $954.05 / 4.7703 = 199.9979. After: the prices sum to $1,118.42. Set the new divisor so the level is unchanged: D_new = $1,118.42 / 199.9979 = 5.592159. Equivalently D_new = D_old x (new sum / old sum) = 4.7703 x 1.172287. Leaving the divisor alone would print a level of 234.4549, a move of 17.229% that no holder experienced. This is exactly how the Dow divisor drifted from 1 to well under 0.2.
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example
A trading floor has 40 people on it. What is the chance that at least two share a birthday, as a percentage?
Answer 89
There are C(40,2) = 780 pairs, each matching with probability 1/365. P(none) ≈ e^−2.14 ≈ 0.12, so about 88%.
Symmetry arguments
Questions that collapse to one line once you notice the two cases are mirror images.
Example
How many ways can 4 items be chosen from 11 when order does not matter?
Answer 330
C(11,4) = 330. The ordered count would be 4! = 24 times larger.
Reading the question exactly
At least, exactly, and given that - the three phrases that change the answer entirely.
Example
A sum of 18,000 is lent for two years at 9% a year. How much more does compound interest earn than simple interest?
- 145.8
- 1,620
- 3,240
- 291.6
Answer 145.8
Over two years the gap is the interest earned on the first year's interest: P x (r/100)^2 = 18,000 x 0.09^2 = 145.8. The principal and the first year's interest are identical under both schemes.
What a good score looks like
On a paper of 15 questions with no penalty for a wrong answer, the only thing an unanswered question can do is cost you. Probability rounds are usually marked as part of a wider battery, so a standalone threshold is rarely reported. Where candidates do describe one it clusters around getting two thirds of the items right, with the caveat that these sections are short enough that two mistakes move you a long way.
How to train for it
- 01Work the standard results until they are recall, not derivation: complement, conditional, binomial mean and variance, geometric expectation.
- 02Practise setting up before calculating. Most wrong answers on these are a correct calculation of the wrong quantity.
- 03Do them timed. A probability question you can solve in four minutes and the paper gives you ninety seconds for is a question you cannot solve.
TRAIN IT HERE
The drills that match each section
Likelihood Ranking
Order events from most to least likely - the exact screen-question format.
Fermi Estimation
Piano tuners in Chicago, atoms in a body - scored on order of magnitude.
Quitters Never Lose
A casino stopping-strategy game that is secretly a martingale lesson.
Tail Risk
Rare events and fat tails, and what they do to a plain expected-value estimate.
SIT THE FULL BATTERY
All the sections back to back on one clock, marked the way the real screen marks them, with a by-skill breakdown at the end. Included with any pass.
Also reported at Citadel Securities
Common questions
- Is the Citadel Securities probability oa test multiple choice?
- Typed numeric answer, no calculator. You type the number, so there is nothing to eliminate your way to.
- How long is the Citadel Securities probability oa test?
- 15 questions in 30 minutes, which is about 2 minutes each.
- Is there negative marking on the Citadel Securities probability oa test?
- No. A wrong answer costs nothing beyond the mark you would have earned, so leaving an item blank is never better than guessing at it.
- How do I practise for it free?
- Every drill linked on this page is free to play, with no account, inside a daily run cap. Questions are generated fresh each run, so there is nothing to memorise between attempts. The full Citadel Dual Online Assessment sitting puts the sections back to back on one clock.