SIG (Susquehanna) Interview Questions

Aaron, Bryce, and Craig are all of different integer ages. They had the following conversation: (i) Bryce to Craig: 'You're the youngest.' (ii) Aaron to Bryce: 'Your age is exactly 70% greater than mine.' (iii) Aaron to Craig: 'Your age is the average of my age and Bryce's age.' (iv) Craig to Aaron: 'I'm at least 8 years older than you.' However, not all of these statements are true. Whenever speaking to someone older, a speaker always tells the truth; when speaking to someone younger, a speaker always lies. How old is Craig?

Mickey and Minnie plan to meet at a cafe, but each will independently arrive at a uniformly random time between 9:00 and 10:00. Mickey will wait 10 minutes for Minnie before leaving, and Minnie will wait 30 minutes for Mickey before leaving. What is the probability that they meet each other?

Given 5 fair dice, what is the probability of obtaining a result where exactly 3 of the dice show the same value?

For a fair coin, what is the minimum, maximum, and expected (average) number of flips needed to get either 3 heads or 3 tails?

A property has a 10% chance of containing oil, making it worth $1 million, a 30% chance of containing coal, making it worth $500,000, and if no resources are found, it can be sold for $200,000. What is the expected value of this property?

Five guys walk into a bar. In how many ways can they sit so that they are arranged from oldest to youngest?

If you have 8 marbles and one is lighter than the rest, how would you determine which one is lighter using a balance scale in two weighings?

What is the difference between bagging and boosting?

We have three pancakes. One is burnt on both sides, one is burnt on one side, and one is not burnt at all. The pancakes are stacked on a plate so that all that can be seen is a burnt side on top. What is the probability that the fully burnt pancake is the one on top?

There are different levels of smokers, with some being more likely to die than others. If a person has died, what is the probability that they were a heavy smoker?

You are betting $50 on a basketball game and your friend is betting $20. If you win, you gain your friend's $20; if you lose, you forfeit your $50 to your friend. What is your expected profit?

You are playing a game where both you and your opponent have each put $10 in the pot. Your opponent now bets another $10. What is the minimum probability of winning required for you to call this $10 bet?

Pick three numbers between 1 and 20. What is the probability that one of the numbers is the average of the other two?

What is the probability of getting the sequence HHT before HTH when flipping a fair coin repeatedly?

You play a game where you have $100 to split between yourself and a random person. You decide how to split it, and the other person can either accept (so you both receive the split amounts) or refuse (in which case both of you get $0 and the game ends). What split do you propose? What if the amount to split is $1,000,000?

What is the probability of rolling six consecutive 3s with a fair six-sided die?

Suppose we have a $10 bet. At any time, I can ask to double the bet. If you accept, we both put in another $10, so the winner gets $20. If you lose, you forfeit everything; if you reject the double, you lose the initial $10. What is the minimum probability of winning that would make you accept the double?

Suppose you and I are playing a game and have bet $10, which will go to the winner. At some point, I offer to double the bet to $20. If you accept, the game continues with the new bet; if you refuse, you lose the game and forfeit the original $10. What is the minimum probability of winning that you would need to accept the increased bet?

You have two torpedoes to hit a boat. Each torpedo has a 2/3 chance of hitting the boat. If you launch both torpedoes, what is the probability that the boat is hit?

You can roll a fair six-sided die a maximum of two times. After each roll, you can choose to accept the current roll's value or roll again (if it is your first roll). You must accept the value on your last roll. What is the expected value of this strategy?

If you randomly cut a cake n times, what is the expected number of pieces?

What is the average distance between two random points on the circumference of a unit circle?

You toss a fair coin repeatedly. What are the odds that the sequence HTH appears before the sequence HHT?

What is the probability of getting the sequence HTH before HHT when repeatedly flipping a fair coin?

Calculate the probability that a person has a disease given that the test result is positive. What is the probability if the test result is positive twice?

1. A painted 3x3 cube consists of 27 small cubes. If one small cube is selected at random and thrown, and upon landing only its unpainted sides are visible, what is the probability that this cube is completely unpainted? 2. Eight people are sitting around a table. If three are selected randomly, what is the probability that at least two of the selected people were sitting next to each other?

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

Two points are randomly selected on the circumference of 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 is the zero matrix, what is the maximum number of positive entries A can have?

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