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Equation 8 · Part 2 · Ten Failure Modes That Define Production AI Agent Architectures

Symbol q

Pat least one=1−(1−q)k.P_{\text{at least one}} = 1 - (1 - q)^{k}.
qq

What this part means

the probability.

Its job in the formula

q is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

Suppose a supervisor dispatches a task to k subagents running in parallel specifically to shorten wall-clock time, and each subagent independently produces a silently wrong or incomplete result — one that does not raise an error, only a bad answer the supervisor’s synthesis step has to catch — with probability q .

The passage around this formula

…wall-clock time, and each subagent independently produces a silently wrong or incomplete result — one that does not raise an error, only a bad answer the supervisor’s synthesis step has to catch — with probability q . Under an independence assumption that will not hold exactly in practice, because subagents sharing a planner, a toolset, and a training distribution are correlated rather than independent, the probability that at least one branch’s bad output reaches the synthesis step unflagged is [displayed…

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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

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