Unfair Split

What this conditional-expectation interview question tests

This is an easy probability question that probes your ability to reason about conditional expectation—a foundational skill in quantitative finance. Rather than asking for a raw probability, it conditions on an observed outcome and asks you to compute an expected value under that constraint. Firms use questions like this to see whether you can set up and simplify a conditional distribution cleanly.

The core challenge is recognizing that given a global constraint (exactly 3 Heads across all 10 flips), the remaining uncertainty is confined to how those Heads are distributed across the two halves of the sequence. This is a good test of whether you can exploit symmetry and conditional reasoning to avoid heavy computation.

• Conditioning on observed events
• Symmetry and exchangeability
• Linearity of expectation under constraints