Ultimate guide to quant interview questions

Before forgetting everything, here is a short guide for future me if I was to interview for a quant trading position again. It's much easier than people thought, and of course can be learned like any other subject. Breaking it down:

1. Expectation questions:

    a. Given four balls of different color in a bag. Each time you take two balls out and pain one ball the color of the other ball. Expected how many times until all the ball have the same color (HFT)

    b. Given n ropes in a basket. Each time you take randomly two ends and connect them together. Expected how many loops there are at the end (Quant fund)

    c. Toss a dice of 6 faces. Expected how many time until you see all six faces

    There are tons of these questions that I have encounter. The way to answer them is quite simple, conditional expectation. 

E(#loop) = E(#loop | two ends are of the same rope) * Prob(two ends of same rope) + E(#loop | twi ebds are not the same ropes)

Same principle every where. Note that you often ends up with a recursive sequence, where to calculate En you have a formula En = something E(n-1) + something E(n-2). In this case you need to know how to quickly solve recursive sequence too.

2. Beyesian Probability questions
   a. 1000 coins, 999 is normal Head tail coin, one is head head coin. Take a coin out, toss ten times. The result is all ten times was head. What is the probability that the coin taken out was head (Bank - Execution quant)
   These are often described as the tricky / counter intuitive one. Only apply the Beye formula for this.

3. Probability distribution
   a. Given three points in a circle randomly distributed, uniform, independent. What is the probability that they all lie in the same circle

Now there are quite a lot other type of questions. So this guide is not as ultimate as it sounds. Will update in the future may be. Some noticeable examples: CS questions (recommend CareerCup book), control theory question (hard as ****), statistics questions (fit data, least square, max likelihood), game question (finding the best strategy).