optiver | | Interview Experience
Interview Date: Not specified
Result: Not specified
Difficulty: Not specified
Interview Process
The interview consisted of multiple rounds focusing on probability-related questions. The format included both theoretical questions and practical problem-solving scenarios.
Technical Questions
- What is the probability that the next card drawn from a deck is red after discarding the first 10 cards?
- Calculate the probability that the sum of the three smallest numbers rolled on four dice equals 3.
- What is the probability of rolling a sum of 7 with two dice?
- Given an unfair coin with a 60% chance of heads, calculate the probability of winning $20 if betting $1 each time until either winning or losing everything.
- A couple wants more girls than boys. If the first child is a girl, they will not have more children. What is the expected number of children they should have?
- In a 4x4 grid, if A starts from the lower left and B starts from the upper right, what is the probability that they do not meet?
- Determine the probability that the difference of two dice rolls is greater than 2.
- If three two-digit numbers are chosen at random, what is the probability that their sum is a three-digit number?
- What is the expected sum of all rolls until a die shows a number greater than 4?
- What is the probability that the ones digit of a randomly chosen two-digit number is greater than the tens digit?
- Calculate the expected value of the product of three cards drawn from a standard 52-card deck.
- What is the probability that the difference between two randomly chosen three-digit numbers is a two-digit number?
- What is the probability that the sum of two distinct integers chosen from 1 to 9 is 10 or greater?
- If you flip 8 coins, what is the probability that three of the same side appear in a row?
- Starting at the origin and rolling a die, if a roll of 1, 2, or 3 means moving right and 4, 5, or 6 means moving left by X-3, how many rolls on average are needed to be 10 steps away from the origin?
- In a game with 100 flipped coins, where pairs are removed until none remain, what is the fair value of the game?
- Two particles start at opposite vertices of an octagon, moving based on the outcome of flipped coins. How many coins need to be flipped until the particles meet on average?
- If three cards are drawn from a standard deck, what is the probability that they are pulled in non-decreasing order?
- If thirteen cards are drawn from a standard deck, what is the probability that no aces are drawn?
- If three dice are rolled, what is the probability that one or more of the dice can sum to 5?
- A particle starts at the center of a 10x10 grid and can move in any direction with equal probability. How many steps on average does it take to hit the boundary?
- A bag contains 10 red, 10 yellow, and 10 blue balls. What is the expected number of remaining balls when only two colors are left?
- Starting with $10 and rolling a die 10 times, what is the probability of going bankrupt if even rolls add $1 and odd rolls subtract $1?
- Continue rolling dice and summing until the total exceeds 100. What is the probability of achieving this?
Tips & Insights
Focus on understanding the underlying principles of probability and practice solving problems efficiently. Familiarize yourself with common probability distributions and expected value calculations.