All simulators
Inclusion–Exclusion & Fréchet Bounds
Set P(A), P(B) and their overlap; watch the union, the complement and the feasible range of the joint move.
Day 1: Probability Axioms & Set TheoryP(A ∪ B)
0.85
P(A)+P(B)−P(A∩B)
P(neither)
0.15
De Morgan
P(A | B)
0.70
P(A) = 0.70
Fréchet range of P(A∩B)
0.20–0.50
independent: 0.350
A and B are independent: P(A∩B) = P(A)P(B).
The overlap can only move inside the Fréchet bounds (the shaded band). Without linked data, that band is all the marginals tell you.