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Equation 4 · Part 2 · How AI and Cybersecurity Actually Work

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Precision=TPR⋅pTPR⋅p+FPR⋅(1−p)\text{Precision} = \frac{\text{TPR} \cdot p}{\text{TPR} \cdot p + \text{FPR} \cdot (1-p)}
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

A simple way to see why the base rate of genuine misuse matters as much as the detector’s accuracy is the standard result relating a detector’s precision to how rare the thing it is looking for actually is. If a detection system has a true-positive rate TPR\text{TPR} and false-positive rate FPR\text{FPR} , and the true prevalence of the underlying misuse event in the traffic it sees is p , the fraction of flagged events that are genuinely misuse — the precision an analyst actually experiences — is Precision=TPR⋅pTPR⋅p+FPR⋅(1−p)\text{Precision} = \frac{\text{TPR} \cdot p}{\text{TPR} \cdot p + \text{FPR} \cdot (1-p)}. When p is small, which it almost always is for genuine, successful misuse against a well-defended system, precision collapses toward zero even for a detector with a very low…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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