Jane Street Interview Questions

Suppose you are playing a dice game with a six-sided die. You may roll the die as many times as you like, and after each roll, you may choose to stop and take the sum of the numbers rolled as your score. However, if you roll a 6 at any time, you must stop and your total score becomes 0. What is the optimal strategy to maximize your expected score?

What is the probability of getting an odd number of heads when flipping 200 fair coins?

100 coins are flipped in a sequence. What six yes/no questions would you ask to maximize your chance of guessing the sequence?

You are playing a game in which you roll a fair 6-sided die. If you roll n, you get n dollars. How much would you pay for this game? Suppose you may reroll if you're not satisfied with the first roll, but must accept the result of the second roll. Now, how much would you pay for the game? What if you can reroll up to two times? How much would you pay?

What is the probability of getting exactly 4 heads in 9 coin tosses?

If there's a 20% chance of rain on Saturday and a 30% chance of rain on Sunday, what is the probability it rains at least once this weekend?

There are two balls in a bag, each either black or white. If you draw a white ball, put it back, then draw again and it's still a white ball, what is the probability of drawing a white ball the next time?

There are 4 players in a game, each rolling a standard die. The player with the largest value and the player with the smallest value form one team; the remaining two players form the other team. The winning team is the one with the larger sum of their dice values, and their payoff is the difference between the team sums. Analyze the expected payoff of the winning team.

Between rolling a single 20-sided die and rolling the sum of three 6-sided dice, which option gives a better chance of obtaining the highest number?

Can you generate a number from 1 to 10 uniformly at random using two dice?

You have 100 coins. How can you split them into piles such that the product of the number of coins in each pile is maximized? In the general setting, what is the optimal strategy?

What is the probability of getting an odd number of heads when 100 fair coins are flipped?

Develop a strategy for the Colonel Blotto game with 10 battlefields valued from 1 to 10 and 100 soldiers to allocate.

What is the optimal way to bet on the outcomes of a six-sided die roll?

What is the sum of the odd positive integers less than 60? What is the probability that n coins have an even number of heads, and how does this probability change if one of the coins is biased?

In a game where a fair coin is tossed repeatedly, player A wins if the sequence HTT appears first, and player B wins if the sequence TTH appears first. Is this game fair?

Starting from today's date in DD/MM/YYYY format, what is the next date in the future whose digits are all distinct?

What is 5 to the power of 5?

What is the expected value of a game where you roll a fair die and receive the number shown in dollars?

Suppose you are offered the opportunity to bet on a coin flip resulting in heads, with the odds increasing from 1.5:1 up to 7:1. Explain your reasoning for whether you would bet or not bet at each odds level.

Compute the expected value of the median when rolling a fair six-sided die three times.

How many handshakes occur among 8 men in a room if every pair shakes hands?

You are given a deck of cards numbered 1 to 100 and two boxes. For each card, flip a fair coin: place the card in the left box if heads, right box if tails. Find the expected value of the minimum card in the box that contains card 100.

Player A rolls three 6-sided dice. Player B rolls one 20-sided die. The player with the highest score wins. Which player would you prefer to be, and why?

What day of the week is 180 days from today? What is the probability that it will rain on the weekend if there is a 50% chance it will rain on Saturday and a 60% chance for Sunday?

What is the probability of flipping four heads in a row with a fair coin?

If 4 coins are flipped, what is the probability that at most 2 heads are flipped?

A watch was broken into three equal parts, and the sum of the digits on each part was equal. What are the numbers on each of the parts?

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

You roll a die repeatedly until you get a 5. What is the expected value of the minimum value rolled during this process?