Jane Street Interview Questions

Given n unbiased coins, what is the probability that exactly half of them are heads? Answer the question for n = 2, 3, and 20,000.

Given two fair dice, what is the probability that both show six if it is observed that at least one die shows a six?

What is 15% of 115?

A has 5 fair coins and B has 4 fair coins. A wins only if he flips more heads than B does. What is the probability that A wins?

Given 5 pumpkins and the sum of the weights of every pair of two pumpkins, determine the weight of each individual pumpkin.

Suppose there are n people on a bus. At each of three stops, 2/3 of the people on the bus get off and 7 people get on. What is the minimum number of people that were initially on the bus before the first stop, given that the number of people on the bus remains an integer after each stop?

You flip 4 fair coins and receive x dollars, where x is the square of the number of heads. What are your expected winnings?

What is the sum of the odd numbers between 1 and 100?

What is 2,000,000 minus 1,011?

What is 37 times 37?

If there are N points on a circle and a chord is drawn between each pair of points, how many regions does the circle get subdivided into?

What is 38 squared?

Consider the following game: You are given a 12-sided die and will be paid the number that the die lands on. If you are unhappy with the roll, you may instead choose to roll two 6-sided dice and will be paid the sum of those two dice. What is the expected value of this game, and how much would you be willing to pay to play?

In Linux, how can you find the total number of files in the current folder, including all subfolders?

If two equally talented teams are playing in the World Series, what is the probability that the series lasts seven games?

A bus pulls up to a stop. Three-quarters of the people get off and seven people get on. The bus goes to two more stops with the same results. What is the smallest number of people that could have initially been on the bus?

You and a friend are betting on individual games of the World Series. For each game, if your team wins, you win a certain positive amount of money, and if your team loses, you lose that same amount. You and your friend want to construct a betting scheme so that you will win $1000 if your team wins the series and lose $1000 if your team loses the series, regardless of the final game score (e.g., 4-3, 2-4, etc.). How much should you bet on the first game?

On an infinite chessboard, to how many possible positions can a knight move after 10 moves? Provide a 90% confidence interval. Is the actual answer even or odd?

Player A had a better batting average than Player B in both the first and second halves of the season. Is it possible for Player B to have a better average than Player A over the entire season?

Apples cost 27 cents each. How many apples can you purchase with $10? (Solve this in under one minute.)

If you roll a 10-sided die and a 20-sided die, what is the probability that the 10-sided die shows a higher number than the 20-sided die?

A steel ball with an 8 cm diameter weighs 8 ounces. How much does a steel ball with a 12 cm diameter weigh, assuming both balls are made of the same material?

You throw a die two times. What is the probability of getting at least one six?

We play a game where we each guess the sum of two dice rolls. Whoever's guess is closest to the actual outcome wins. What would your optimal strategy be?

You want to buy a car at an auction where the car's price is uniformly distributed between $0 and $1000. If you bid more than the car's price, you win it at the price you bid; if you bid less than the car's price, you do not win it but also do not lose anything. You can sell the car for 1.5 times the value for which you bought it. What should you bid to maximize your expected profit?

You have two packs of poker cards: one with 52 cards, the other with 104 cards. You will pick two cards separately from the same pack. If both cards are red, you win. Which pack should you choose to maximize your chances of winning?

I roll a die and will give you an amount in pounds equal to the number on the die. For example, if I get 5, I will give you 5 pounds. What is the price you are willing to pay for this game?

What is the sum of the digits of all the numbers from 1 to 1,000,000? This is different from the sum of the numbers. For instance, the sum of the numbers from 1 to 10 is 55, whereas the sum of the digits is 46.

What is 87 multiplied by 46?

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