First question: Weather report says there is a 30% chance of rain on Saturday and 30% chance of rain on Sunday. What can you say about the probability that it rains on at least one of the days?
Quantitative Researcher Intern Interview Questions
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Coupon collector problem.
About coin tossing game
Easy conditional probability question
What is the expected value of a 3d6 roll?
Throw a die with 6 faces two times. You may guess whether their sum is even. If you guess right, you win one dollar. What is your expected earn?
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.
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