Complex Probability with Dependent and Independent Events with conditional

14 Views Asked by At

Can I make the simplification: P(D | A ∩ B ∩ C) = P(D | A) ? And if yes, please may i have the proof please ? Or a book where I can find it ?

When : D is independant of B and C but it is dependant of A.

And my question in a more largest way : I have to calculate P(A ∩ B ∩ C ∩ D) and I know P(A ∩ B ∩ C) and P(D | A).

For example we can say : I want the probability of picking a woman, in this country, this age, this height.

A : Be a woman B : Which country C : Age D : Height

Thank you for all