Thread: law 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)

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