PRACTICE GUIDE HEADLANDS
Headlands Probability & Estimation Practice Test
This guide offers probability & estimation preparation for readers interested in Headlands Technologies. The general practice ranges below are not a verified assessment specification for that employer.
Those are ranges across firms running this format rather than Headlands Technologies's own figures, so treat them as the shape to train against and check the instruction screen on the day for the marking rule.
Outcry is not affiliated with Headlands Technologies 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 Headlands Technologies’s own.
What it screens
A Chicago-based quantitative trading firm making markets in listed derivatives.
- ✓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 Headlands Technologies
A Chicago-based quantitative trading firm making markets in listed derivatives. The topics here are Outcry preparation suggestions, not a verified firm syllabus or recruiting stage.
Outcry also has 1 other topic guides for readers interested in Headlands Technologies. Their presence does not mean applicants must sit that many tests or that they belong to one recruiting round.
The format
These are general practice ranges, not a verified current assessment specification for Headlands Technologies. Check the employer’s invitation for the actual format.
| 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 | Preparation topics · employer round unconfirmed |
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 Headlands Technologies’s.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example
A market is Calm or Volatile. Each day: Calm turns Volatile with probability 0.1, Volatile turns Calm with probability 0.3. Over the long run, what fraction of days are Calm?
- 1/4
- 3/4
- 1/2
- 9/10
Answer 3/4
Stationarity balances the flows: π(Calm)·0.1 = π(Vol)·0.3, so π(Calm) = 0.3/(0.1+0.3) = 3/4.
Counting and combinatorics
Arrangements, selections and the complement trick that turns a hard count into an easy one.
Example
A 4-sided die is rolled until it shows a 4. The first 4 on roll n pays $4^n. The game is stopped after 9 rolls and pays nothing if no 4 has come up. What is the expected payout?
Answer 9841
The first 4 lands on roll n with probability (3/4)^(n-1) x 1/4, and that roll pays $1 x 4^n. Multiplying gives $1 x 3^(n-1), so the terms grow rather than shrink and the sum over the 9 rolls is $9841. Same shape as St Petersburg: the payout outruns the probability, so only the cap keeps the expectation finite.
Distributions you should know cold
Binomial, geometric and uniform means and variances, applied rather than quoted.
Example
A walker takes 6 steps, each equally likely left or right. What is the chance of ending exactly where it started?
- 62.5%
- 31.25%
- 50%
- 12.5%
- 16.67%
Answer 31.25%
It needs exactly 3 of each direction: C(6,3) = 20 out of 2^6 = 64, which is 31.25%.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
A. exactly one tail in four coin flips B. a die roll of 5 or more C. a heart or a spade from a full deck
Rank most likely to least likely:
- B > A > C
- A > B > C
- A > C > B
- C > B > A
Answer C > B > A
A: 25.0% · B: 33.3% · C: 50.0%
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example
An index rises 2.3% on 5 days and falls 2.3% on 5 other days. What is the net change over the 10 days, as a percentage?
Answer -0.26
Each up-down pair multiplies to 1 − 2.3%² = 1 − 0.05%. With 5 pairs the drag is about −5 × 0.05% = -0.26%.
Symmetry arguments
Questions that collapse to one line once you notice the two cases are mirror images.
Example
A fair coin is flipped 4 times. What is the chance every flip is heads, as a percentage?
Answer 6.25
(1/2)^4 = 1/16 = 0.063, or 6.25%.
What a good score looks like
No current employer cutoff is verified for these general practice ranges. Use the worked examples to identify what to study and check your role-specific invitation for the actual assessment rules.
How to train for it
- 01Practise setting up before calculating. Most wrong answers on these are a correct calculation of the wrong quantity.
- 02Do 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.
- 03Work the complement first whenever the question says at least or at most. It is usually the shorter route and it is almost always the intended one.
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 Headlands Technologies
Common questions
- Is the Headlands probability & estimation test multiple choice?
- This guide uses multiple choice or a typed number for practice. The employer’s current answer format was not verified here.
- How long is the Headlands probability & estimation test?
- This guide uses general practice ranges of 10 to 20 questions in 15 to 45 minutes. They are not a verified current employer format.
- Is there negative marking on the Headlands 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?
- The warm-up drills are free with no account, and every pass opens the rest of the drills linked on this page. Questions are generated fresh each run, so there is nothing to memorise between attempts.