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Equation 8 · Part 5 · Ten Failure Modes That Define Production AI Agent Architectures

subtraction

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

What this part means

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

Its job in the formula

Subtract the following term or group from the preceding one. A leading minus marks a negative quantity.

The passage around this formula

The trade-off has a clean, if deliberately simplified, shape. 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 . 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 Pat least one=1−(1−q)kP_{\text{at least one}} = 1 - (1 - q)^{k}. This is…

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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the surrounding passage

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