I haven't had a proofs class, so proofs always seem so complex to me. Here's the question: If A,B, and C are mutually independent, show that the following pairs of events are independent: A' and (B and C') (I understood the other ones). Also show that A', B', and C' are mutually independent.

Here's as far as I could get for the first part:

P(A') and P(B and C') = P(A') P(B) P(C')

1-p(a) and p(b) and (1-p(c))= p(a' and c') and p(b)

p(b)-p(a)p(b)(1-p(c))=(paUc)' and p(b)=

p(b)-p(b)p(c)-p(a)p(b)+p(a)p(b)p(c)=

For the second part I proved that each pair of a,b,c was independent, but I can't get very far with all three mutually independent. I know that p(a' and b' and c')= p(a')p(b')p(c') and then I multiplied out the first part taking the compliment of each as (1-p(x)) and multiplying the three.

I would really appreciate and help with this topic a lot! Thanks!