7 problems
Expected value interview questions
Games, stopping rules and recursive expectations. Interviewers want to see you set up the recursion before you reach for arithmetic.
Roll a die, take it or reroll
Warm-upYou roll a fair six-sided die and may either keep the value or reroll once and keep the second value. What is the optimal strategy and its expected value?
The larger of two dice
StandardTwo fair six-sided dice are rolled. What is the expected value of the larger?
Cards until the first ace
HardYou deal a shuffled 52-card deck one card at a time. What is the expected number of cards dealt before the first ace appears?
Collecting the full set
StandardA cereal brand hides one of six equally likely toys per box. How many boxes until you expect to own all six?
When to stop looking
HardYou interview n candidates in random order, learn only relative ranks, and must accept or reject each immediately. How do you maximise the chance of hiring the best one?
Gambler's ruin
StandardYou start with 10 and bet 1 per round on a fair coin, stopping at 0 or at 20. What is the probability you reach 20, and how long does the game last on average?
Uniforms until the sum passes one
HardYou draw independent uniform numbers on [0,1] and stop when their sum first exceeds 1. How many draws do you expect to make?