Could someone help me with a probability proof real quick?

[Jay59express]

here is the question: If A and B are independent events, show that A' and B are also independent [Hint: First estalish a relationship between
P(A' n B), P(B), and P(A n B).
I know that if A and B are independent, P(A)*P(B) = P(A n B), and that P(A') = 1 - P(A), but after that I am stuck. The only thing i know is that I need to prove that P(A') * P(B) = P(A' n B).
Could someone shed some light on me about this? Thanks in advance

 

[rob3rt]

ok check this out. Now, by AB i mean A union B, its easier for me to write it that way

Assume that A and B are independent. Now, look at those circle diagrams and convince yourself that A=AB U AB'.

A = AB U AB'
P(A) = P(AB) + P(AB') since AB and AB' are mutually exclusive
P(A) = P(A)P(B) + P(AB') since A and B are independent, thus

P(AB') = P(A)[1 - P(B)]
P(AB') = P(A)P(B').

Then, A and B' are independent.

 

[Rarr]

Yep.

 

[Jay59express]

Thanks a bunch guys