Three faces of a tetrahedron are painted red (R), green (G) and blue (B), while the forth face is painted in all three colors (see the figure). Denote by P (A) the probability that it falls on a face containing the color A, A = R, G, B.
The source also includes Figure 6 showing the tetrahedron; Flash preserves only the textual face-color description.
Check if \(P ( A \cap B ) = P ( A ) P ( B )\) for all \(A , B = R , G , B\)
Check if \(P ( R \cap G \cap B ) = P ( R ) P ( G ) P ( B )\) . Are the events R, G, B pairwise independent? Are they mutually independent?