FA-6350 / Statistics / Member archive

Probability union with overlap · case 05

The overlapping event mass is counted twice.

Member previewVariant 5 · 3 implementations · 4 checks per implementation

Case contract

Integer finite observations and equal lengths for paired samples. Counts and weights are nonnegative. Rational results use reduced Fraction strings. Empty or undefined statistics return None where shown. a,b,overlap are rational strings for valid probabilities with max(0,a+b-1)<=overlap<=min(a,b); do not assume independence. Exact operational definition: str(Fraction(a)+Fraction(b)-Fraction(overlap))

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Statistical estimators results depend on the stated convention.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
fixture 1: ('1/2', '1/2', '1/4')	`"1"`	`"3/4"`	Failed

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