Jane Street Interview Questions

You have a drawer with an infinite number of socks in two colors, with each color equally likely. What is the expected number of socks you must draw individually from the drawer before you obtain a matching pair?

If I flip 100 coins and then multiply the number of heads by the number of tails, what is the expected value of that product? Can you provide a confidence interval for this value?

I play a game where I start with a score of 100. I then flip 10 coins in a row. Every time I get a head, I add 1 to my score. When I get a tails, I take the reciprocal of my score. If you are running this game, and people are given their score in pounds at the end of the game, how much would you charge people to play?

In the game 'Shut the box', what is the average score a player achieves by the end if they play using the optimal strategy? How does this average score change if, instead, the player makes random moves?

The date is written as DD/MM/YYYY. What is the closest date that will use at most one digit throughout the date?

Decompose 300,000 into its prime factors. Then, arrange all the digits from these prime factors to form the smallest possible number.

a) The odds of having pizza on a Saturday are 60%, and on Sunday, 30%. What are the odds of having pizza at least once during the weekend? b) How do the odds change if you are only allowed pizza on one of the two days? c) What if you can only have pizza on Sunday if you had it on Saturday first?

Find the smallest positive integer x such that the product of all the digits of x is 10,000.

Two teams are playing a best-of-7 tournament. Each team has a 50% chance of winning each game. What is the probability that the series reaches the 7th game?

You have all the clubs from a standard deck (13 cards). You can choose 2 cards and receive a payout equal to their product, where all face cards are valued at 0. You may pay $1 to reveal the difference between any two cards of your choice. What is the expected value you should be willing to pay to play this game?

If you have balls weighing 1g, 2g, ..., up to 40g, and you have a fair balance, what is the minimum number of their weights you need to know in advance so that you can measure all the others?

How can you create a fair coin using an unfair coin? Is there any method that ensures you do not waste any of your coin flips during the process?

If we flip a coin 100 times, what is the probability of getting an even number of heads?

There are an unknown number of people on a bus. At the first stop, three-quarters of the passengers get off and 7 people get on. This process repeats for two more stops. After this sequence, what is the minimum possible number of people that could be on the bus?

What is the result of multiplying 17 by 3.3?

An asymmetrical 12-sided die has a 40% chance of rolling a 12, and the remaining faces are equally likely. Two people each choose a number between 1 and 12. The person whose chosen number is closer to the result of the die roll wins. Which number should you choose to maximize your chances of winning?

Two dice are rolled, and the result is hidden, but it is known that at least one die shows a 6. What is the expected value of the sum of the two dice?

You have a standard deck of 52 cards. I draw a card and tell you I drew a heart. Now you draw a card from the remaining cards. What is the probability that you will also draw a heart? Again, you have a standard deck of 52 cards. I draw 13 cards and tell you I drew exactly 5 hearts. Now you draw 13 cards from the cards that are remaining. What is the expected number of hearts you will draw?

1. What is the probability of getting a head when flipping a fair coin once? 2. What is the expected value of the sum obtained when flipping 8 fair coins, where a head counts as 1 and a tail as 0?

What is the minimum number of people needed in a room so that at least five of them share the same birth month?

Imagine I flip 100 coins in sequence, and you must guess the exact sequence. You can ask one yes/no question. What question should you ask to maximize your probability of correctly guessing the sequence?

What is the probability of getting at least 4 heads in 7 coin flips?

Devise a betting strategy for a seven-game series such that if team 1 wins the series, you win $1000 no matter what, and if team 1 loses the series, you lose $1000 no matter what.

It is 10:45 in London. What is the angle, in degrees, between the hour and minute hands of a clock at this time?

Find the sum of all odd numbers between 1 and 50. Then, how many 4-digit numbers can be made using the digits 1, 2, 3, and 4 (with or without repeating digits), and what is their average?

If 1.5 chickens lay 1.5 eggs in 1.5 days, how many eggs do 9 chickens lay in 9 days?

A fair coin is flipped repeatedly. If the sequence HHT appears before HTT, player A wins. Otherwise, player B wins. What is the probability that player A wins?

Given two bowling balls of the same density, if one weighs X kg and has a diameter of 10 inches, and the other has a diameter of 16 inches, how much does the second ball weigh?

You and your opponent play a coin-flipping game. If the first player flips heads, the second player pays him $30. If the first player flips tails, the coin passes to the second player, who then flips. If the second player flips heads, he wins $30 from the first player. This process continues. How much should you pay to go first?

Given a fair six-sided die (faces numbered 1 to 6), what is the expected value of a single roll? Suppose you have two chances: after the first roll, you can choose whether to keep the result or roll again. What is the maximum expected value you can achieve if you use the best possible strategy?