multiplication

The passage around this formula

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 $\tau$ — a deleted database rather than a clumsy sentence — is $q_\tau = \Pr(\text{failure and severity} > \tau) = (1-p)\cdot \Pr(C > \tau \mid \text{failure})$. The success rate p says nothing at all about the second factor. Two agents can share an identical p of 0.99 while their conditional severity distributions, $\Pr(C > \tau \mid \text{failure})$ , differ by…

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