Calculating Complex Joint Probability with Dependent and Independent Events

23 Views Asked by At

Can I make the simplification: P(D | A ∩ B ∩ C) = P(D | A) ?

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

And my question in a more largest way :

How can I calculate the probability P(A ∩ B ∩ C ∩ D ∩ E ∩ F) when:

D depends only on A. E is independent of all events. F also depends on A. B and C depends on A and C depends on B also.

Can I just say that : P(A∩B∩C∩D∩E∩F)=P(A)⋅P(B∣A)⋅P(C∣A,B)⋅P(D∣A)⋅P(E)⋅P(F∣A)