passCaretK function

double passCaretK(List<bool> trialPasses, int k)

Anthropic: probability that all k trials pass.

pass^k = (c / n)^k for the empirical estimator. Some references use the unbiased combinatorial form C(c, k) / C(n, k). We provide the empirical version because it's intuitive and consistent with how teams report "X out of Y trials passed" in CI reports.

Returns 0.0 when k <= 0 or n == 0.

Implementation

double passCaretK(List<bool> trialPasses, int k) {
  final n = trialPasses.length;
  if (k <= 0 || n == 0) return 0.0;
  final c = trialPasses.where((p) => p).length;
  if (c == 0) return 0.0;
  // (c/n)^k
  return _pow(c / n, k);
}