Independence Without Pairwise

Problem

A regular octahedron has faces numbered $1$ – $8$ ; one throw gives sample space $\Omega = \{1, \dots, 8\}$ (uniform). Construct events $A, B, C$ with

P(ABC) = P(A)P(B)P(C),

but such that $A, B, C$ are not pairwise independent.

Answer

Solution

Difficulty	7/10
Topics	Set Theory, probability, Casework

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