The shorter pattern loses

What this pattern-matching probability question tests

This is a hard probability question that asks you to reason about competing stochastic processes — specifically, the race between two patterns to appear first in a sequence of fair coin flips. It is the kind of problem quant firms use to assess whether a candidate can set up and solve a non-obvious conditional probability problem under time pressure.

The core challenge is to model the state space carefully. You must track not just whether each target pattern has appeared, but also the progress toward each pattern at every step of the sequence. This typically requires either a system of equations (using first-step analysis and the law of total probability) or a Markov chain with states representing partial matches. The key insight is recognizing which states are absorbing, transient, or reflecting, and how transitions between them depend on coin-flip outcomes.

• First-step analysis and recursive probability equations
• Markov chains and state-space design for pattern problems
• Conditioning on the history of flips and overlap structure
• Competing processes and race-to-absorption problems