PRACTICE GUIDE TOWER RESEARCH
Tower Research Probability & Estimation Practice Test
This guide offers probability & estimation preparation for readers interested in Tower Research Capital. The general practice ranges below are not a verified assessment specification for that employer.
Those are ranges across firms running this format rather than Tower Research Capital's own figures, so treat them as the shape to train against and check the instruction screen on the day for the marking rule.
These are Outcry preparation topics, not a verified current firm assessment specification. Check your role-specific invitation for the test, timing, tools and recruitment stage.
Outcry is not affiliated with Tower Research Capital 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 Tower Research Capital’s own.
What it screens
A quantitative trading firm whose public careers material covers trading, research and engineering.
- ✓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 Tower Research Capital
A quantitative trading firm whose public careers material covers trading, research and engineering. The topics here are Outcry preparation suggestions, not a verified firm syllabus or recruiting stage.
Outcry also has 2 other topic guides for readers interested in Tower Research Capital. 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 Tower Research Capital. 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 Tower Research Capital’s.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example
X counts heads in 400 flips of a coin that lands heads 50% of the time. What is Var(X)?
Answer 100
Binomial variance np(1−p) = 400·0.5·0.5 = 100.
Estimation under uncertainty
A number nobody knows exactly, reasoned to the right order of magnitude out loud.
Example
51 bars sit on the bench. They all weigh the same except one, which is heavier. A balance compares two groups and reports which side is heavier, or that they match. How many weighings are needed in the worst case?
Answer 4
Each weighing has three outcomes, so w weighings can separate at most 3^w cases. Here 3^3 = 27 is below 51 and 3^4 = 81 is not, so 4 is the floor. It is also reachable: split into three groups as equal as you can, weigh two of them, and the heavy bar is in a group of at most 17. Repeat.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
A. exactly one head in three coin flips B. a black ace from a full deck C. at least one six in three die rolls
Rank most likely to least likely:
- C > A > B
- B > A > C
- C > B > A
- B > C > A
Answer C > A > B
A: 37.5% · B: 3.8% · C: 42.1%
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example
A bet pays 1.5 to 1 and wins 57% of the time. What fraction of the bankroll does Kelly stake, as a percentage?
Answer 28
f = (bp − q)/b = (1.5 × 0.57 − 0.43)/1.5 = 0.28, so about 28% of the roll.
Symmetry arguments
Questions that collapse to one line once you notice the two cases are mirror images.
Example
400 lamps start off. Person k flips every kth lamp, for k from 1 to 400. How many lamps end on?
Answer 20
A lamp ends on when it has an odd number of divisors, which happens only for perfect squares. Up to 400 there are 20 of them.
Reading the question exactly
At least, exactly, and given that - the three phrases that change the answer entirely.
Example
In a code, HEDGE is written as JGFIG. How is YIELD written in the same code?
- AKGNF
- WGCJB
- DLEIY
- BLHOG
Answer AKGNF
Every letter moves forward 2 places in the alphabet: H becomes J. Applying the same shift to YIELD gives AKGNF.
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
- 01Work the standard results until they are recall, not derivation: complement, conditional, binomial mean and variance, geometric expectation.
- 02Sanity-check the magnitude before committing. A probability above one or an expectation outside the range of outcomes is a caught error, and these papers plant both as options.
- 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 Tower Research Capital
Common questions
- Is the Tower Research 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 Tower Research 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 Tower Research 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.