Dueling Stock I

What this competing-outcomes probability question tests

This is a medium-difficulty probability problem that combines conditional reasoning, infinite series, and absorbing states. It's representative of questions quant firms use to probe how candidates set up and solve problems involving asymmetric competition and eventual resolution.

The core challenge is recognizing that the process continues until at least one outcome is "absorbed"—a terminal state—and then computing probabilities under that constraint. Candidates must track multiple competing pathways, handle the possibility of repeated trials, and solve for steady-state or limiting probabilities. Clean problem setup and algebraic clarity matter more than speed; interviewers watch for whether you identify the key insight (what conditions end the process) before diving into calculation.

• Absorbing states and Markov chains
• Geometric series and infinite repeated trials
• Conditional probability under competing outcomes
• Solving systems of recursive equations