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What this consecutive-outcome probability question tests

This is a medium-difficulty probability question that asks you to find an expected value when the stopping condition involves a pattern rather than a single event. It is a classic interview question at quant trading and quantitative research firms because it rewards both clean problem setup and the ability to handle recurrence relations.

The key insight is to define states based on progress toward the goal—how many consecutive heads have you just flipped—and then write equations that relate the expected number of flips from each state. This approach scales to any pattern and teaches you to think recursively about probabilistic processes.

• State-space formulation for stochastic processes
• Recurrence relations and systems of linear equations
• Symmetry and conditioning on the last flip