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1−p1-p

Why this formula appears here

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 ≥\geq 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 τ\tau — a deleted database rather than a clumsy sentence — is

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pp

Symbol p

its failure probability, and let severity be a random quantity C ≥\geq 0 describing how bad a given failure turns out to be, conditional on failure occurring.

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1−p1-p

Equation 2 · Model Evaluation

Why Average Success Rate Hides the Failures That Matter Most

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

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 ≥\geq 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 τ\tau — a deleted database rather than a clumsy sentence — is

Meanings in this article

  • pp: its failure probability, and let severity be a random quantity C ≥\geq 0 describing how bad a given failure turns out to be, conditional on failure occurring.
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1−p1-p

Equation 1 · AI Safety

Ten Failure Modes That Define Deployed AI Safety Systems

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text.

The failure modes built on repeated querying — jailbreak search, paraphrase evasion, mismatched-language generalisation — share a further structural property worth stating precisely, because a single strong per-attempt success rate is often reported as though it settled the question of robustness on its own. Suppose a safeguard blocks a fixed, independently generated attack attempt with probability 1-p , so a single try succeeds only with probability p . An adversary who is not limited to one try, and who runs k independent attempts — exactly the loop PAIR and the suffix-search method both implement mechanically [ 2 , 1 ] — succeeds at least once with probability

Meanings in this article

  • pp: the probability.
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