SIG (Susquehanna) Interview Questions

If you roll two dice and add their results, what is the probability of obtaining a sum of 6?

Compress a string such that repeated characters are replaced by the character followed by the number of repetitions. For example, given 'AAABBCC', output 'A3B2C2'.

Write a method that returns a stock ticker value based on a company name found within a string of text, which may also contain random words in addition to the company name. Optimize the method for performance, assuming there could be millions of companies to search through.

Calculate the probability of having a disease given that a diagnostic test result is positive. What is the probability if the test result is positive twice?

Is 1599 a prime number?

A painted 3x3 cube consists of 27 small cubes. If one small cube is selected at random and thrown, and you observe only the unpainted sides, what is the probability that the selected cube is completely unpainted?

Nine white cubes are arranged into a 3x3 cube and the outside surfaces are painted green. A cube is randomly selected and rolled. If the side facing up is white, what is the probability that this cube was the middle (center) cube?

Two points are uniformly distributed around the circumference of a unit circle. What is the expected value of the distance between them?

A deck of 18 custom playing cards is numbered from 1 to 18. A card is drawn 6 times with replacement. If X is the number of draws that result in a prime number, what is the expected value of X (E(X))?

Two points are randomly selected on a circle. What is the expected distance between them?

Given an n-by-n real matrix A where every entry is nonnegative and A squared (A^2) is the zero matrix, what is the maximum number of positive entries that A can have?

If you break a unit stick randomly at two points, what is the expected length of the smallest piece?

Three real numbers are chosen independently and uniformly at random from the interval [0, 3]. What is the probability that the smallest number is between 0.5 and 1?

You are a player on a basketball team that is losing by 2 points. You have the ball, and there are 3 seconds remaining. You have two options: pass to a teammate for a 3-point shot (with a 37% probability of making it and winning the game), or pass for a 2-point shot (with a 77% probability of making it and tying the game). In the event of a tie, your team goes to overtime, where there is a 50% chance of winning. What should you do, and why?

A boat fires torpedoes at another boat. The probability that a torpedo hits is 1/3. If a torpedo hits the boat, the boat is destroyed. Two torpedoes are fired. What is the probability that the ship is destroyed?

You have 17 coins and I have 16 coins. We flip all the coins at the same time. If you have more heads than I do, you win; if we have the same number of heads or you have fewer, then I win. What is your probability of winning?

You roll a die and win twice the value of the face if it is even, or the face value if it is odd. What is the fair amount to charge to play this game? If you are given the option to roll again and will only be paid based on the result of the second roll if you choose to roll again (i.e., the result of the last roll), what is the fair charge to play the game with this option?

Every morning, Mike the security guard at CP High School opens all 1000 doors in the building, numbered 1 to 1000. The next guard closes all even-numbered doors. Each subsequent guard toggles (opens if closed, closes if open) every nth door, where n is the guard's number, until the 1000th guard toggles only door 1000. How many doors are left open in the end?

What is the expected value of a single roll of a fair six-sided die?

I have a painting. If it is an original, it is worth $500,000; if it is not, it is worth $10,000. The probability that it is an original is 0.2. I have an option to pay $100,000 for the painting after inspection. What is the value of this option?

You start with 1 dollar and your friend starts with 2 dollars. You bet 1 dollar per round until one of you runs out of money. Each round, you have a 2/3 chance of winning the bet. What is the probability that you win all your friend's money before losing yours?

Given a multiplication table showing values such as 2^2, 2^3, and so on, estimate the range for the value of 14^7 divided by 5^3.

We are playing Russian roulette with a standard 6-chamber revolver. Two bullets are placed in adjacent chambers. I spin the cylinder, point the gun at my head, and pull the trigger. I survive. Now it's your turn. You can either (a) re-spin, aim at your head, and pull the trigger, or (b) not spin, aim at your head, and pull the trigger. Which option gives you a higher chance of survival? Additionally, given that I spun the cylinder, what is the probability that I die this time?

A group of people wants to determine their average salary on the condition that no individual is able to discover anyone else's salary. How can they accomplish this?

Which is larger: 2 to the power of 1/3 or 10 to the power of 1/10?

A submarine is targeted by two torpedoes, each with a 1/3 probability of hitting the target independently. What is the probability that at least one of the torpedoes will hit the submarine?

You have five friends of different ages going to dinner. What is the probability that they will sit in age order around the table, either clockwise or counterclockwise?

You have 1,000 bottles of wine, one of which is poisoned. You have a number of slaves you can use for testing, and you want to minimize the number of deaths while guaranteeing you find the poisoned bottle. The poison is fast-acting and fatal within an hour, and you have just over an hour before your guests arrive. Each slave can taste test any number of bottles. What strategy will allow you to find the poisoned bottle using the fewest number of slaves?

Solve for x in the equation x^{x^{x^{...}}} = 2, where the power tower extends infinitely.

Given an array of integers and an integer k, find the k-th largest element in the array.