Facing chickens

What this expected-value puzzle tests

This is an easy probability question that tests your ability to use linearity of expectation to solve a counting problem elegantly. Rather than enumerating all possible configurations, the insight is to break the problem into independent pieces and sum their contributions.

Quant firms ask questions like this because they reveal whether you can spot structure in a seemingly complex setup. The skill being tested is recognizing when a problem can be decomposed into simpler subproblems, each with the same underlying probability, rather than attempting brute-force enumeration. This approach scales well and generalizes to much larger instances.

• Linearity of expectation over independent indicator random variables
• Symmetry and identical distributions
• Reducing a global counting problem to local interactions