SIG (Susquehanna) Interview Questions

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?

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?

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?

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?