use the law of total probabilty to prove that

a. if P (A l B) = P (A l B,) then A and B are independent

b. if P (A l C ) > P (B l C) and P (A l C' ) > P( B l C' ), then P (A) > P (B)

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- Jan 30th 2010, 01:21 AMstressedoutlaw of total probability
use the law of total probabilty to prove that

a. if P (A l B) = P (A l B,) then A and B are independent

b. if P (A l C ) > P (B l C) and P (A l C' ) > P( B l C' ), then P (A) > P (B) - Jan 30th 2010, 01:47 AMMoo
Hello,

The law of total probability says that

So here, since B and B' are complementary events.

Provided that , it follows that

For the second one... :

But from the two inequalities, we can say that , and the RHS is exactly