// QUANT INTERVIEW PREP
Probability Quant Interview Prep & Practice
Probability is the core of almost every quant interview, from the online assessment to the final round. These questions cover conditioning, Bayes' rule and counting, the three ideas most screens come back to.
Sample Probability Questions
Question 1 · Optiver Trading Assessment
A market quotes odds of 4-to-1 against an event. What is the implied probability?
- 400%
- 20%
- 25%
- 80%
Question 2 · SIG Problem-Solving Assessment
A drawer holds 63 fair test coins and one that has heads on both faces. One is taken out at random and tossed 6 times. It comes up heads every time. What is the probability that it is the two-headed one?
See the solution ↓Question 3 · Five Rings Quant Trading Screen
A surveillance rule flags 93% of genuine breaches and also fires on 4% of clean accounts. 0.4% of accounts are genuine breaches. A flag just fired - what is the chance the account is a genuine breach, as a percentage?
See the solution ↓Question 4 · Old Mission Quant Screen
A game show hides a prize behind one of 6 doors. You pick a door. The host, who knows where the prize is, then opens every other door except one, all of them empty, and offers you the switch. What is the probability you win if you switch?
- 41.7%
- 83.3%
- 50%
- 16.7%
Question 5 · Belvedere Technical Challenge
A desk of 5 traders and 7 analysts must send 3 traders and 2 analysts to a meeting. How many different groups are possible?
See the solution ↓
Step-by-Step Solutions
Solution 1
A market quotes odds of 4-to-1 against an event. What is the implied probability?
Answer: 20%
Odds of 4-to-1 against means 1 favourable out of 5 total: 1/5 = 20%.
Solution 2
A drawer holds 63 fair test coins and one that has heads on both faces. One is taken out at random and tossed 6 times. It comes up heads every time. What is the probability that it is the two-headed one?
Answer: 0.5039
Bayes, with the prior 1/64 on the two-headed test coin. The two-headed one gives 6 heads with probability 1; a fair one gives 6 heads with probability 1/2^6 = 1/64. Posterior odds are prior odds times the likelihood ratio: (1 to 63) x (64 to 1) = 64 to 63. As a probability that is 64/(64 + 63) = 0.5039. Every extra head doubles the odds, so the evidence compounds fast.
Solution 3
A surveillance rule flags 93% of genuine breaches and also fires on 4% of clean accounts. 0.4% of accounts are genuine breaches. A flag just fired - what is the chance the account is a genuine breach, as a percentage?
Answer: 9
Take 10,000 accounts: about 37 genuine ones get flagged and about 398 clean ones do. 37/436 ≈ 9%.
Solution 4
A game show hides a prize behind one of 6 doors. You pick a door. The host, who knows where the prize is, then opens every other door except one, all of them empty, and offers you the switch. What is the probability you win if you switch?
Answer: 83.3%
Your first pick is right 16.7% of the time and nothing the host does changes that. All the remaining probability, 83.3%, has been squeezed onto the one door he left closed. Switching takes it.
Solution 5
A desk of 5 traders and 7 analysts must send 3 traders and 2 analysts to a meeting. How many different groups are possible?
Answer: 210
Choose the traders and the analysts separately, then multiply: C(5,3) = 10 and C(7,2) = 21, so 10 × 21 = 210. Order inside each group does not matter, which is why this is a combination and not a permutation.
How to Pass the Probability Screen
Write the sample space before you compute anything. Most wrong answers come from counting the wrong outcomes, not from bad arithmetic.
For conditional questions, name the event you are conditioning on and shrink the space to it. Bayes is just that step written as a formula.
Sanity-check the size of your answer. A probability above one, or a rare event you made likely, is the cheapest error to catch and the most common one to submit.
Practice probability alongside 4,000+ more procedurally generated scenarios under live timer conditions. Unlock Outcry Pro.
More Prep Tracks
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