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Equation 5 · From Autocomplete to Delegation: The Technical History Behind OpenAI Codex

What does this equation mean?

pass@⁡k=1−(1−p)k.\operatorname{pass@}k=1-(1-p)^k.

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Inputs and operations1-(1-p)^k
Result or conditionpass@k
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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kk

Symbol k

k is part of the quantity the equation computes from the expression on the right.

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pp

Symbol p

the success probability.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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superscript

superscript

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

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How to interpret it

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What the article says around this equation

The sampling result made the search interpretation explicit. If independent candidates have success probability p , the chance of at least one success among k is pass@⁡k=1−(1−p)k\operatorname{pass@}k=1-(1-p)^k. Real samples are not independent and the paper used estimators appropriate to its setup, but the conceptual point holds: model probability plus an evaluator can search a program space. Without a reliable selector, many candidates become review burden.

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Sources cited in the article section

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