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Equation 12 · Part 4 · Measuring AI Agent Reliability: What the Evidence Actually Supports

Symbol n

passk  :=  Etasks ⁣[ (ck)(nk) ]\text{pass}^{k} \;:=\; \mathbb{E}_{\text{tasks}}\!\left[\, \frac{\binom{c}{k}}{\binom{n}{k}} \,\right]
nn

What this part means

the two formulas share the same.

Its job in the formula

n appears inside an expected value, so its contribution is averaged under the distribution or condition shown by that operator.

Where the article explains it

The two formulas share the same n , c , and k and the same combinatorial machinery, and that similarity is precisely the point: they are estimating two different probabilities from the same data, one about the best of k attempts and one about the consistency of all k of them.

The passage around this formula

…under domain policies, proposed the complementary statistic: the probability that every one of k independent trials on the same task succeeds, rather than at least one of them [ 3 ] . The two formulas share the same n , c , and k and the same combinatorial machinery, and that similarity is precisely the point: they are estimating two different probabilities from the same data, one about the best of k attempts and one about the consistency of all k of them. A system can score well on the first and badly on the…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.