Jane Street Interview Questions

What is the probability of drawing two red cards in succession from a standard deck of 52 cards and from a double deck of 104 cards?

An unfair die with 12 faces has the number 11 with a probability of 40%, while the other faces are equally likely. You and another player are playing a game where whoever is closer to the correct answer wins. What is your optimal strategy, and should you choose to go first or second?

How much would you pay to play a game where you roll a die and receive the number of dots rolled in dollars?

You pick n points independently and uniformly at random on the circumference of a circle. 1. What is the probability P(n) that all n points lie within some semicircle of the circle? 2. Simplify your answer to a closed form in terms of n.