SIG (Susquehanna) Interview Questions

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

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.

Flip coins sequentially until the sequence 'HT' or 'TT' appears. What is the probability that 'HT' appears before 'TT'?

A frog is traveling from point A(0, 0) to point B(4, 6). Each step can only be 1 unit up or 1 unit to the right. The frog refuses to move three steps in the same direction consecutively. Compute the number of ways the frog can move from A to B.

A painting is on sale for X amount. The probability that it is real is Y. If it is real, it is worth A; if it is a fake, it is worth B. What is the expected gain on purchasing this painting?

Given a standard shuffled deck of cards, you draw a card from the top. How much would you bet that the next card is higher than the one you drew? Please discuss bet sizing strategies and whether the order of the cards matters.

You have $100 and receive an additional $100 to play a casino game where you bet on flips of a fair coin, with a 4:5 payout. You are required to bet a total of at least $500 before you can cash out. How do you maximize your expected earnings?

A can finish a job in 100 minutes, and B can finish the same job in 120 minutes. A and B work together on the job, but after 40 minutes, C comes to help them, and they finish the job in an additional 10 minutes. How long would it take C to finish the job by himself?

What is the expected number of times you need to roll a die to get a 6?

What is the fair price to enter a game where you win the amount shown on a single rolled die?

Person A completes a job in 100 minutes. Person B completes the same job in 120 minutes. They work together for 30 minutes, then person C joins. Together, the three complete the job in another 20 minutes. How long would it take for person C to complete the job alone?

A painting has an 80% chance of being fake. If it is real, it is worth $500,000; if fake, it is worth $10,000. The seller asks for $120,000. Based on this information, should you buy the painting?

Given the probabilities of an event occurring on each of two days, find the probability that the event occurs on at least one of those days.

In a population, 50% do not smoke, 20% are light smokers, and 30% are heavy smokers. Heavy smokers are twice as likely to die as light smokers, and light smokers are twice as likely to die as non-smokers. What is the probability that a person was a heavy smoker given that they have died?

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