Citadel Interview Questions

How would you construct an options position that is long vega and short gamma?

What is the probability of finding two consecutive ones in a randomly generated binary string of length n, where each bit is equally likely to be 0 or 1?

What is the probability of picking two diamonds and one card that is not a diamond from a standard deck of 52 cards?

Suppose I have two pancakes: one with both sides burnt, and one with one burnt side and one unburnt side. I randomly choose one pancake, then randomly look at one of its sides. If the side is burnt, what is the probability that I picked the pancake with both sides burnt?

What is the probability of getting a three-of-a-kind in Texas Hold'em poker?

How do you generate a uniform distribution over a disk given access to two independent uniform random variables?

What is the expected value of the cube of a fair six-sided die roll?

Given a matrix of size N by T, where the entry at the i-th row and j-th column represents the price of buying i shares of a stock at time j, determine the minimum total cost of purchasing N shares by the end of time T.

You are given two ropes that, when lit, each burn for exactly one hour, but not necessarily at a constant rate. Which one of the following times CANNOT be measured using these ropes? a) 50 minutes b) 30 minutes c) 25 minutes d) 35 minutes.

Explain why the volatility smile exists.

You are tossing a fair coin. What is the expected number of tosses until you get two heads in a row?

If 0.1% of people have a certain disease, and you have a test that is correct 99% of the time, what is the probability that someone who tests positive actually has the disease?

What is the expected value of the sum when rolling two fair six-sided dice?

Given a biased coin (with probability p of landing heads), what is the probability of flipping two heads (HH) in two consecutive tosses?

Describe how the random forest algorithm works.