Optiver Interview Questions

What is the result of dividing 3/4 by 1/2? Show your calculations.

What is the expected value of the sum of the values of three randomly selected cards from a standard deck of 52 playing cards?

How would you calculate the final price of an asset in a trading simulation given historical trading data?

Given four numbers, use arithmetic operations (+, -, ×, ÷) to make 24. Each number must be used exactly once.

What is the next number in the sequence: 1, 16, 7, 100, 13?

What is the expected value of a dice rolling game where you roll two standard six-sided dice, receive the sum of the two dice unless both show the same number, in which case you receive 0?

How would you price an asset, given a list of bids and asks?

How many cards are needed to build a 100-storey house of cards, assuming each storey is constructed in the standard way?

Out of 100 fair coin flips, what is the probability that you get at least 10 more heads than tails?

Implement a linear regression algorithm from scratch, without using any machine learning libraries.

Roll a die repeatedly until you obtain either a 5 or a 6. If you roll a 5, you cash out the sum of all previous rolls, excluding the 5. If you roll a 6, you receive no payout. You are allowed to cash out mid-game for the sum accrued up to that point. How can you maximize your expected payoff?

Given a simulated order book, how would you determine the fair value of a derivative?

What is the total number of ways to arrange 3 red balls, 7 blue balls, and 9 green balls in a line?

In a family, the parents continue having children until they have more girls than boys. What is the expected number of children in this family?

If you flip 100 fair coins, what is the variance of the number of Heads?

Divide 2 by 17 to four decimal places without using any calculator or external materials.

An interviewer will play Padel against me. The interviewer, being better, has a 70% chance to win a point against me. The game is played to 11 points, but a player must win by at least 2 points. The current score is 9 to 9. What is the probability that I win the game?

Estimate how many ways there are to add three positive integers to obtain a sum of 25.

You have 16 watermelons and a seesaw. What is the minimum number of tests required to determine the two heaviest watermelons?

Six people are sitting around a circle. What is the probability that they are seated in increasing order of age, either clockwise or counterclockwise?

A group of people wants to determine their average salary on the condition that no individual can find out anyone else's salary. Can they accomplish this, and if so, how?

Two people each flip a fair coin 4 times. What is the probability that both people end up with the same number of heads?