## Problem 272 — rank:259

**Title:** Fail-safe biocontainment

**Added binding assumptions (LaTeX):**

```latex
Define the independent exposure unit and account for shared ancestry and environmental dependence; cells from one culture are not automatically independent escape trials. For zero events in $n$ independent complete-detection trials at one condition, the one-sided binomial upper bound is $1-\alpha^{1/n}$, illustrating the sample-size cost of a small claim. Multiple conditions and imperfect detection require adjusted simultaneous bounds. No observed escapes is not proof of zero probability.
```

**Direct edits:** 0. **Fresh external checks:** None; supplied sources retained as provenance.