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Equation 8 · Part 1 · AI for Science and Medicine in Practice: An Advanced Technical Guide

Symbol P

P(at least one success in k)=1−(1−p)k,P(\text{at least one success in } k) = 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

Batch size interacts with the value of parallel experiments in a way worth costing out explicitly. If a single proposed experiment succeeds with probability p , and a batch of k proposals were independent, the probability that at least one succeeds is P(at least one success in k)=1−(1−p)kP(\text{at least one success in } k) = 1 - (1-p)^{k}. which is why both systems ran in batches — parallel throughput converts a low per-attempt success probability into a high per-batch one. Two caveats matter in practice: proposals drawn from the same model on the same pool are correlated, so realised batch success rates fall short of this bound, and a larger batch is only worth its cost if throughput, not sample count, is the bottleneck actually being relieved.

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Learn the underlying idea

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

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Sources cited in the article section

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