Multiplication Rule of Probability

\(B_1\) \(B_2\)
\(A_1\) \( P(A_1 ∩ B_1 )\) =
0
\( P(A_1 ∩ B_2 )\) =
 
\( P(A_{1})\) =
0 1
\(A_2\) \( P(A_2 ∩ B_1 )\) = \( P(A_2 ∩ B_2 )\) = \( P(A_{2})\) =
\( P(B_{1})\) =
0 1
\( P(B_{2})\) =
 

\(B_1\) \(B_2\)
\(A_1\) \( P(B_1 | A_1 ) = \frac{P(A_1 ∩ B_1 )}{P(A_{1}) } = \) \( P(B_2 | A_1 ) = \frac{P(A_1 ∩ B_2 )}{P(A_{1}) } = \) 1.00
\(A_2\) \( P(B_1 | A_2 ) = \frac{P(A_2 ∩ B_1 )}{P(A_{2}) } = \) \( P(B_2 | A_2 ) = \frac{P(A_2 ∩ B_2 )}{P(A_{2}) } = \) 1.00