Equation 4 · Why Average Success Rate Hides the Failures That Matter Most
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Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol τ
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What the article says around this equation
It helps to state the structural point precisely rather than just by example. Let p be an agent’s probability of completing a task successfully, so 1-p is its failure probability, and let severity be a random quantity C 0 describing how bad a given failure turns out to be, conditional on failure occurring. The probability that a given run produces a failure whose severity clears some consequential threshold — a deleted database rather than a clumsy sentence — is
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