Probabilities and independence

dionys 101 Oct 16, 2004 at 23:10

Can you help plz..
i dont know how to prove this:

A,B,C are 3 independent events.
We must prove that A and BUC are independent too

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Ed_Mack 101 Oct 16, 2004 at 23:34

hmm, let me sketch this out:

To prove A and BuC are in dependant, BuC must equal BuC A
(BTW, is given, so BuC given A must equal BuC)
General: X Z = (XnZ) / Z
BuC A = (BuC n A) / A

When A and B dependant , AnB = A|B * B
When A and B independent AnB = A*B

BuC | A = (BuC * A) / A
BuC | A = BuC
Therefore, BuC is independant of A

(I hope that’s what you’re after)