← All parts of this equation

Equation 19 · Part 3 · Why Average Success Rate Hides the Failures That Matter Most

superscript

(1−qτ)n(1-q_\tau)^n
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Suppose an evaluation runs n independent trials of a consequential task and observes zero failures above the severity threshold τ\tau . It is tempting to read that as evidence the risk is negligible. It is not, and the size of the gap has a name: the rule of three. If the true failure probability is qτq_\tau , the probability of observing zero events in n independent trials is (1-qτq_\tau)^n ; setting that probability equal to 0.05 and solving gives n ln⁡(1−qτ)\ln(1-q_\tau) ≈\approx -3 , and for small qτq_\tau , where ln⁡(1−qτ)\ln(1-q_\tau) ≈\approx -qτq_\tau , this reduces to the boundary

Read this part in the article →

Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.