Question 1

You throw a standard die repeatedly, keeping a running total of the sums. What is the probability that when the running total exceeds 100 for the first time, the last die throw is a 2?

Accepted Answer

This is a real Optiver interview question for Quant Researcher roles. Get the full solution and detailed walkthrough by signing up for Quant Blueprint's interview preparation program.

Question 2

Six dice are rolled simultaneously. What is the probability that the sum of the numbers shown is an even number?

Accepted Answer

This is a real Optiver interview question for Graduate Quantitative Researcher roles. Get the full solution and detailed walkthrough by signing up for Quant Blueprint's interview preparation program.

Question 3

Provide a formal proof for the following: You have two groups of marbles—one group with 1 marble and the other with 2^n marbles. At each step, you can double the size of one group by taking marbles fr...

Accepted Answer

This is a real Optiver interview question for Graduate Quantitative Researcher roles. Get the full solution and detailed walkthrough by signing up for Quant Blueprint's interview preparation program.

Question 4

What is the expected number of card draws before encountering an Ace in a standard 52-card deck, assuming cards are drawn one at a time without replacement?

Accepted Answer

This is a real Optiver interview question for Graduate Quantitative Researcher roles. Get the full solution and detailed walkthrough by signing up for Quant Blueprint's interview preparation program.

Question 5

What is the expected number of moves required to exit the center of a 10x10 grid, assuming you can move one step in a random direction (up, down, left, right) at each move?

Accepted Answer