Simple (?) question on conditional probability

Hi, All,

I've searched the old posts and haven't come across the answer to this question. Notation: P is probability; A, B, C, D, and E are random variables; and "&" means "and".

Suppose I know: P(A), P(E|A), P(C|A&E), P(B|A&C), and P(D|C&E).

What is P(A&B&C&D&E)?

I realize that P(A&C&E)=P(A)*P(E|A)*P(C|A&E), but I start to wonder about "double counting" when I get to the more complex problem above.

Thanks for helping,
Grant
.

Loading