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Published equation contexts

Pmiss=(1−rA)(1−rB)P_{miss} = (1-r_A)(1-r_B)

Why this formula appears here

Say check A independently has recall rAr_A against a real defect — the fraction of the time it would catch that class of problem if it ran — and check B has recall rBr_B . If the two checks fail for unrelated reasons, the chance a defect slips past both is the product of the chances it slips past each: Pmiss=(1−rA)(1−rB)P_{miss} = (1-r_A)(1-r_B). which is smaller than either (1-rAr_A) or (1-rBr_B) alone: real, additive protection. But if the two checks share a failure mode — most obviously, if the “second check” is the same model re-reading its own output inside the same context, primed by the same reasoning that produced the mistake — their misses stop being independent, and the joint miss probability climbs back toward…

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PmissP_{miss}

Symbol P_miss

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

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Pmiss=(1−rA)(1−rB)P_{miss} = (1-r_A)(1-r_B)

Equation 5 · AI Agents & Systems

How Verification Actually Works in a Claude Code Workflow

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Say check A independently has recall rAr_A against a real defect — the fraction of the time it would catch that class of problem if it ran — and check B has recall rBr_B . If the two checks fail for unrelated reasons, the chance a defect slips past both is the product of the chances it slips past each: Pmiss=(1−rA)(1−rB)P_{miss} = (1-r_A)(1-r_B). which is smaller than either (1-rAr_A) or (1-rBr_B) alone: real, additive protection. But if the two checks share a failure mode — most obviously, if the “second check” is the same model re-reading its own output inside the same context, primed by the same reasoning that produced the mistake — their misses stop being independent, and the joint miss probability climbs back toward…

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