PRACTICE GUIDE BELVEDERE TRADING
Belvedere Trading Probability and Logic Practice Test
Outcry’s Belvedere Trading probability and logic practice section has 14 questions in 25 minutes. These numbers describe the linked mock; the source check below distinguishes published details from practice settings.
Our combined mock includes both skill tracks. Trader candidates should treat coding as supplementary; 14 maths questions, two coding tasks and the clocks are Outcry settings.
Outcry is not affiliated with Belvedere Trading 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 Belvedere Trading’s own.
What it screens
A Chicago-based proprietary trading firm specialising in options market making and derivatives strategies.
- ✓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 Belvedere Trading
Belvedere’s campus process places a timed technical challenge after application. It specifies probability and logic for traders, or coding for developers.
Practice stage: Initial technical challenge · firm process Step 2. Our combined mock includes both skill tracks. Trader candidates should treat coding as supplementary; 14 maths questions, two coding tasks and the clocks are Outcry settings.
The format
These are the settings used by Outcry’s Belvedere Trading practice sitting. They are not automatically the employer’s published format; see the linked assessment’s source check.
| Questions | 14 |
|---|---|
| Time | 25 minutes |
| Per question | 1.8 minutes |
| Negative marking | No |
| Answer style | Typed numeric answer, no calculator |
| Where it sits | Initial technical challenge · firm process Step 2 |
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 Belvedere Trading’s.
Expected value and odds
Pricing a bet, converting between odds and probabilities, and deciding whether to take it.
Example
You roll a fair die 3 times. Probability of at least one six?
- 50%
- 32.1%
- 42.1%
- 0.5%
Answer 42.1%
Complement: 1 − (5/6)^3 = 42.1%. Adding 1/6 each time double-counts.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example
A strategy's daily returns over n days average x̄ with sample standard deviation s. Which statistic tests whether the true mean return is zero?
- x̄ / (s/√n)
- x̄·√n / s²
- (x̄ − s) / n
- x̄ / s
Answer x̄ / (s/√n)
The one-sample t-statistic divides the observed mean by its standard error s/√n. Dividing by s alone ignores how the estimate sharpens with n.
Estimation under uncertainty
A number nobody knows exactly, reasoned to the right order of magnitude out loud.
Example
4 crates arrive at a receiving dock holding spacers, shims, gaskets and bolts, one content each. Each crate carries a label naming one of those 4 contents, no two labels the same, and every label is on the wrong crate. Opening a crate shows what is in it. How many crates must be opened, in the worst case, to relabel all 4 correctly?
Answer 2
The label-to-contents map is a permutation with no fixed point, and there are 9 of those on 4 items. Opening a crate reveals its contents and splits the live set; picking the next crate after seeing the last result, a minimax search over every opening order gives 2 as the worst case. With 4 = 3 the two possible arrangements are the two rotations, and one look separates them. The general pattern: the last two crates settle themselves only when the two contents left both clash with their own labels.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
A. a queen from a full deck B. two dice summing to 6 C. exactly two tails in four coin flips
Rank most likely to least likely:
- C > B > A
- A > C > B
- B > C > A
- A > B > C
Answer C > B > A
A: 7.7% · B: 13.9% · C: 37.5%
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%.
Symmetry arguments
Questions that collapse to one line once you notice the two cases are mirror images.
Example
Three fair dice are rolled. How many of the 216 ordered outcomes total 7?
Answer 15
Counting ordered triples summing to 7 gives 15, so the chance is 15/216 = 6.9%.
What a good score looks like
Use this mock’s score and worked review to identify skills to practise. No Outcry score guarantees a pass or a hiring outcome; a current employer threshold for this practice paper has not been verified.
How to train for it
- 01Practise setting up before calculating. Most wrong answers on these are a correct calculation of the wrong quantity.
- 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 Belvedere Trading
Common questions
- Is this Belvedere Trading’s official probability and logic test?
- No. Outcry generates its own questions. Belvedere’s campus process places a timed technical challenge after application. It specifies probability and logic for traders, or coding for developers. Our combined mock includes both skill tracks. Trader candidates should treat coding as supplementary; 14 maths questions, two coding tasks and the clocks are Outcry settings.
- How long is this probability and logic practice section?
- 14 questions in 25 minutes in the Outcry mock. These are practice settings unless the source check explicitly confirms them.
- How is the practice marked?
- Correct answers earn 1 mark unless the question states another weight. Wrong answers lose 0; unanswered items lose 0, including timeouts. These rules apply to this mock.
- Where can I check the employer’s process?
- See the public source check on the linked assessment. Your role-specific invitation governs the actual format, permitted tools and scoring.