I have two non-mutually exclusive events with probability $P(A)$ and $P(B)$. In addition, I am given the intersection of both events: $P(A \cap B)$
Is it then valid to say:
P(A' \cup B') = 1 - P(A) - P(B) + P(A \cup B)
Using the following identities:
P(A' \cup B') = P(A') + P(B') - P(A' \cap B') P(A') = 1 - P(A) P(B') = 1 - P(B) P(A' \cap B') = P((A \cup B)') = 1 - P(A \cup B)
The big thing I'm not sure about here is the use of DeMorgan's laws to simplify the intersection. Does this all look right?