Equation 12 · Part 10 · Measuring AI Agent Reliability: What the Evidence Actually Supports
Denominator: binomnk
What this part means
The complete quantity below the fraction bar; it must be nonzero for this division.
Its job in the formula
binomnk occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Full expression→Denominator: binomnk→Article meaning
The passage around this formula
Pass@k answers a specific question: given a budget of k independent attempts, what is the chance that at least one succeeds? That is the right question for a search-and-verify workflow, where a cheap checker can identify the one attempt that worked among several candidates. It is the wrong question for almost everything else an agent does, because most agentic tasks do not offer a free, cheap oracle that can pick the winning attempt out of a pile of candidates after the fact — the “attempt” is the deployment. For that setting, Yao and colleagues, building the tau-bench benchmark for tool-using agents interacting with simulated customers under domain policies, proposed the complementary…
Learn the underlying idea
A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.
Open the illustrated fractions: division written vertically guide →
Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.