PRACTICE GUIDE CTC
CTC Probability & Estimation: what the test is, and how to train for it
Chicago Trading Company does not publish the shape of its probability & estimation screen, and candidates describe it as 10 to 20 questions in 15 to 45 minutes, roughly one to three minutes per question, answered by picking one of the options.
Those are ranges across firms running this format rather than Chicago Trading Company's own figures, so treat them as the shape to train against and check the instruction screen on the day for the marking rule.
CTC's own careers page describes this as an aptitude assessment testing critical-thinking skills - candidates report it running heavier on verbal reasoning (synonyms, analogies, odd-one-out) than any other screen on this list, alongside the arithmetic and probability.
Outcry is not affiliated with Chicago Trading Company 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 Chicago Trading Company’s own.
What it screens
A Chicago-based derivatives trading firm making markets in options, futures and other listed products.
- ✓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 Chicago Trading Company
A Chicago-based derivatives trading firm making markets in options, futures and other listed products. What that means for the screen is that the questions tend to be drawn from the work rather than from a textbook, so the format below is the shape to train against rather than a syllabus.
The format
Chicago Trading Company does not publish this screen's shape, and it varies between firms, so these are the ranges candidates report rather than exact figures.
| Questions | 10 to 20 |
|---|---|
| Time | 15 to 45 minutes |
| Per question | one to three minutes |
| Negative marking | Varies by firm and year |
| Answer style | Multiple choice or a typed number |
| Where it sits | First round, or a second technical screen |
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 Chicago Trading Company’s.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example
Roll a fair die until every face has appeared at least once. What is the expected number of rolls?
Answer 14.7
Coupon collector: 6·(1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6) = 14.7.
Counting and combinatorics
Arrangements, selections and the complement trick that turns a hard count into an easy one.
Example
A deck has 11 ranks with 5 cards of each rank, 55 cards in all. You are dealt 5. How many different 5-card hands contain exactly four cards of one rank and one card of a different rank?
Answer 2750
Product rule again. Pick the repeated rank 11 ways, pick four of its 5 cards C(5,4) = 5 ways, then the loose card is any of the 50 cards outside that rank. 11 x 5 x 50 = 2,750.
Distributions you should know cold
Binomial, geometric and uniform means and variances, applied rather than quoted.
Example
Two return series correlate at 0.5. What share of the variance in one is explained by a linear fit on the other?
- 100%
- 75%
- 25%
- 70.7%
- 50%
Answer 25%
R² is the square of the correlation: 0.5² = 0.25, so 25%.
Estimation under uncertainty
A number nobody knows exactly, reasoned to the right order of magnitude out loud.
Example
10 people have to get across a river. The boat carries at most 2 and somebody has to row it back each time. Every crossing counts as one trip, in either direction. What is the fewest trips that gets all 10 across?
Answer 17
Count the net progress. A crossing over plus a row back moves 2 across and brings 1 home, a net gain of 1, and costs 2 trips. After 8 such rounds 8 people are across and 2 are left, which the final crossing takes in one go. So 2 x 8 + 1 = 17.
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example 1
How many digits does 50! have?
Answer 65
Stirling: log10(50!) ≈ 50·log10(50/e) + ½·log10(2π·50) = 63.23 + 1.25 = 64.48, so 65 digits.
Example 2
How many observations are needed for a 95% confidence interval of half-width 2.5, when the standard deviation is 25?
Answer 385
n = (1.96σ/w)². Call it 2: (2 × 25/2.5)² = 400, which overshoots by 4%.
Example 3
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%.
Reading the question exactly
At least, exactly, and given that - the three phrases that change the answer entirely.
Example
A puts in 3,000 for 4 months and B puts in 13,000 for 9 months. They clear 33,000 of profit. What is A's share?
- 16,500
- 10,153.85
- 6,187.5
- 3,069.77
Answer 3,069.77
Profit follows capital multiplied by time. A contributes 3,000 x 4 = 12,000 and B contributes 13,000 x 9 = 117,000, so A takes 12,000 / 129,000 of 33,000 = 3,069.77.
What a good score looks like
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.
Common questions
- Is the CTC probability & estimation test multiple choice?
- Reported as multiple choice or a typed number. Formats move, so treat this as the shape rather than a guarantee.
- How long is the CTC probability & estimation test?
- Candidates report 10 to 20 questions in 15 to 45 minutes, roughly one to three minutes per question.
- Is there negative marking on the CTC probability & estimation test?
- It varies by firm and by year. Where a paper does mark negatively, skipping beats guessing; where it does not, answer everything. Check the instruction screen before you start - it is always stated there.
- 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.