IMC Trading Interview Questions

Two teams are playing each other, and both have positive (plus) odds to win. How much should you bet on each team, and why?

You and a taxman are playing a game with N cards, each labeled with a natural number from 1 to N. You can pick a card only if at least one of its factors is still on the table, and for every card you pick, the taxman takes all available factors of that card from the table. How do you maximize your score?

When rolling a fair six-sided die repeatedly, what is the probability that, before rolling any odd number, you have rolled each even number (2, 4, and 6) at least once?

In a beer pong game with a 4x4 arrangement of cups, each time you land a ball in a cup, both the row and the column containing that cup are removed. Assuming each throw lands in any remaining cup with equal probability, what is the probability that you win the game in the minimum possible number of throws?

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

Derive the Central Limit Theorem for a sequence of independent coin tosses.