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Equation 8 · Part 3 · 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

the probability.

Its job in the formula

p is one of the signed contributions combined to compute the quantity on the left.

Where the article explains it

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}.

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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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