Flipping Until Heads

What this geometric-distribution interview question tests

This is a medium-difficulty probability question that appears regularly in quant interviews. It probes whether you can reason about infinite series and geometric distributions without getting lost in the algebra. The setup is simple, but the solution requires either a clever observation or careful summation.

Candidates typically approach this by writing out the probability of needing exactly 1 flip, exactly 3 flips, exactly 5 flips, and so on, then summing the resulting series. Alternatively, some recognize a structural symmetry that makes the calculation immediate. Interviewers care less about which method you choose than about whether you can justify each step and simplify your final answer.

• Geometric series and their closed forms
• Tail probabilities and recursive reasoning
• Symmetry arguments in probability