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Equation 4 · Part 1 · Ten Failure Modes That Define Deployed AI Safety Systems

Symbol P

P(at least one success in k tries)=1−(1−p)k.P(\text{at least one success in } k \text{ tries}) = 1 - (1-p)^k.
PP

What this part means

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

Its job in the formula

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

The passage around this formula

…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 P(at least one success in k tries)=1−(1−p)kP(\text{at least one success in } k \text{ tries}) = 1 - (1-p)^k. At p = 0.05 , a safeguard that looks 95% reliable per…

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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