Probabilities and independence

[dionys]

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
link (http://www.mathgoodies.com/forums/topic.asp?TOPIC_ID=18007)

[Ed Mack]

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

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

(I hope that's what you're after)