Show that if events A and B are independent, then events A' and B are independent.

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- Jan 11th 2009, 02:03 PMYanshow that events are independent
Show that if events A and B are independent, then events A' and B are independent.

- Jan 11th 2009, 05:56 PMLast_Singularity
If events are independent, then we know that

by definition. That's our key.

For the proof, we will use the following lemma:

Proof of the lemma:

So now we know that lemma is true, we can use it to conclude that:

Looking at the right hand side, we have:

(using our key assumption)

So we conclude that

as desired.

- Jan 11th 2009, 06:31 PMPlato
- Jan 11th 2009, 06:35 PMmr fantastic