Let A and B be two events, show that:
P(A) + P(B) -1 P(A U B) P(A)+P(B)
Am I supposed to assume that A and B are the only events in the sample space, and that therefore P(A)+P(B)=1?
If I assume that, and begin the proof with the first axiom of probability, I get this far:
1. 0 P(A) 1
2. P(A)+P(B)=1 (Since P(S)=1, where P(S) is the sample space)
3. 0 P(A) P(A) + P(B)
There's a couple things I can do from here but it seems to make things more complicated than they need to be.
Thanks for any help in advance!