← All parts of this equation

Equation 5 · Part 3 · From Autocomplete to Delegation: The Technical History Behind OpenAI Codex

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

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

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

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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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

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