Lucky Streak at the Trading Desk

What this stopping-time probability question tests

This is a medium-difficulty probability problem that asks you to reason about a two-agent process with a compound stopping condition. It is typical of the kind of expectation-value questions quant trading firms use to assess whether a candidate can model dynamic, multi-state systems and compute expected stopping times.

The core skill being tested is the ability to set up and solve a system of equations for expected values across multiple states. You must identify the relevant states (how many lucky days each trader has accumulated), write expressions for the expected time from each state, and handle the stopping condition carefully. Problems like this reward clear state-space thinking and systematic bookkeeping over computational speed.

• Markov chains and state transitions
• Systems of linear equations for expected values
• Stopping times and stopping conditions
• Independence and joint probability