Jane Street Interview Questions

You have 4 coins. You throw them in the air. For every coin that lands heads, you get 1 dollar. How much would you pay to play this game?

You are playing a game in which four fair coins are flipped, and the amount of money you receive in dollars equals the number of heads that appear. If you do not like the outcome of the first four flips, you may re-flip all four coins, but you must accept the result of the second set. Determine the fair value for the game.

In Russian Roulette, there is a revolver with 4 blanks and 2 bullets loaded consecutively in adjacent chambers. If the person before you fires a blank (the gun did not discharge), should you take the next shot as-is, or spin the cylinder before shooting? Justify your answer with probabilities.

What is the smallest number made up of only 1s and 0s that is divisible by 225?

What is the expected value of a die roll? Additionally, create a market (bid-ask spread) based on your expectation.