PRACTICE GUIDE DA VINCI
Da Vinci Probability & Estimation Practice Test
Da Vinci 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 Da Vinci'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 Da Vinci 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 Da Vinci’s own.
What it screens
A derivatives market maker in Amsterdam trading options across European and Asian markets.
- ✓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 Da Vinci
A derivatives market maker in Amsterdam trading options across European and Asian markets. 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.
Candidates also report 3 other screens at Da Vinci, covered separately on this site. Where a firm runs several, they usually sit in one round rather than spread across the process, so the pacing of the whole set matters more than any single section.
The format
Da Vinci 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 Da Vinci’s.
Expected value and odds
Pricing a bet, converting between odds and probabilities, and deciding whether to take it.
Example
A market quotes odds of 4-to-3 against an event. What is the implied probability?
- 75%
- 57.1%
- 42.9%
- 133.3%
Answer 42.9%
Odds of 4-to-3 against means 3 favourable out of 7 total: 3/7 = 42.9%.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example
Cards are dealt one at a time from a shuffled standard deck. Before each card you may call "red" - you win if that card is red, and the game ends. If you never call, the last card decides. What is your best possible probability of winning?
- It grows with patience
- 27/52
- 26/51
- 1/2
Answer 1/2
A martingale argument: whatever the strategy, the proportion of reds remaining is a martingale, so every stopping rule wins with exactly 1/2. No timing edge exists.
Counting and combinatorics
Arrangements, selections and the complement trick that turns a hard count into an easy one.
Example
A desk shows 5 quotes, each hit independently with probability 50%. What is the probability that exactly 2 of them are hit? Answer as a percentage.
Answer 31.3
Binomial: C(5,2) x 0.5^2 x 0.5^3 = 10 x 0.25 x 0.125 = 31.3%. The C(5,2) counts which quotes were the ones hit.
Distributions you should know cold
Binomial, geometric and uniform means and variances, applied rather than quoted.
Example
How many ways can 2 people be chosen from 9, order not mattering?
- 72
- 36
- 9
- 45
- 18
Answer 36
C(9,2) = 36. The ordered count 72 overcounts by 2! = 2.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
Spot is 0.9590 dollars per euro. The 12-month dollar rate is 6.04% and the 12-month euro rate is 2.82%, both simple. How many pips are the 12-month forward points, as a signed number?
Answer 300.33
The outright is F = 0.9590 x (1 + 0.0604 x 1.0000) / (1 + 0.0282 x 1.0000) = 0.989033. Forward points are the outright less spot in pips: (0.989033 - 0.9590) x 10,000 = 300.33. Dollar rates are above euro rates, so the euro trades at a forward premium and the points are positive. The sign follows the rate differential and never the view on the currency: a forward is not a forecast.
Reading the question exactly
At least, exactly, and given that - the three phrases that change the answer entirely.
Example
A panel of 4 is picked from 5 engineers and 6 researchers. How many panels contain exactly 2 researchers?
- 5
- 150
- 25
- 330
Answer 150
Choose the researchers, then the engineers: C(6, 2) x C(5, 2) = 15 x 10 = 150. The unrestricted count C(11, 4) = 330 includes every other split.
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
- 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 Da Vinci
Common questions
- Is the Da Vinci 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 Da Vinci 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 Da Vinci 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.