Coin-toss iteration

What this iterative probability question tests

This is a medium-difficulty probability question that combines discrete outcomes with multi-stage reasoning. It asks you to reason about a sequential process where the state space shrinks unpredictably at each step, and to determine the likelihood of a specific terminal condition.

To solve problems of this type, candidates typically need to set up a recurrence relation or use symmetry arguments to avoid enumerating all possible paths. The key insight is recognizing what determines the game's outcome and finding a clean way to compute it without brute-force case analysis. Firms value solutions that are both rigorous and elegant.

• Recursive probability structures and state-dependent outcomes
• Symmetry and invariant properties in sequential processes
• Reasoning about absorbing states and terminal conditions