Suppose P(A∣B)=αP(A|B) = \alphaP(A∣B)=α, P(B∣A)=βP(B|A) = \betaP(B∣A)=β, and P(A∪B)=γP(A \cup B) = \gammaP(A∪B)=γ. Express P(A∩B)P(A \cap B)P(A∩B) in terms of α,β,γ\alpha, \beta, \gammaα,β,γ.
αβγα+β−αβ\frac{\alpha \beta \gamma}{\alpha + \beta - \alpha\beta}α+β−αβαβγ
αβγα+β\frac{\alpha \beta \gamma}{\alpha + \beta}α+βαβγ
αβα+β−γ\frac{\alpha \beta}{\alpha + \beta - \gamma}α+β−γαβ
γαβα+β\frac{\gamma \alpha \beta}{\alpha + \beta}α+βγαβ