A mouse can move one room over within three adjacent rooms in a row each day. You can only check one room. What is the expected number of days it will take to find the mouse? Then, same question but rooms are in a triangle, meaning the mouse can go to either of the two other rooms it is not in.
What strategy would you employ if given the chance to play this game: You receive the amount of dollars shown on the face of a die. You may re-roll the die at most 3 times, but it costs $0.7 to reroll.
You pick n points independently and uniformly at random on the circumference of a circle. 1. What is the probability P(n) that all n points lie within some semicircle of the circle? 2. Simplify your answer to a closed‐form in terms of n.
1. Initial Phone/Zoom Screen • Mental math: Fast, accurate calculations without a calculator (e.g., expected values, probability puzzles, number manipulation). • Logic and probability puzzles: Think of problems involving coins, dice, cards, or Bayesian reasoning. It’s less about prior knowledge and more about thinking out loud and asking the right questions. • Communication: They want to see how clearly and precisely you explain your thought process. 2. Follow-up Technical Interviews • More in-depth problems: These might be longer or more open-ended than the initial screen. They often involve iterating on a solution as the interviewer adds constraints. • Game theory, probability, statistics, estimation questions. • Programming (if applicable): For quant research roles, there might be some Python or OCaml-style thinking, but usually less coding and more algorithmic logic.
mostly probability and logic problems
You flip a coin against me and whoever gets more heads wins. If you can bet money after each coin flip, what is the optimal betting strategy
Probability of raining on sunday or saturday based on individual probabilities. Give upper and lower bounds on the probability of the union.
Alice and Bob each have a coin and flip it until they get a heads. If Bob flipped his coin more times than Alice, what is the expected number of times Alice flipped her coin?
Ask about my programming background as well
the deck of cards question described in other reviews
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