Using the inclusion exclusion principle - http://www.proofwiki.org/wiki/Inclusion-Exclusion_Principle - if I set $n=2$ I get the following -
$P(A_1 \cup A_2) = P(A_1) + P(A_2) - P(A_1 \cap A_2) + P(A_1 \cap A_2)$
when the correct answer should be -
$P(A_1 \cup A_2) = P(A_1) + P(A_2) - P(A_1 \cap A_2)$
I have the term $P(A_1 \cap A_2)$ at the end the first equation due to the last part of the inclusion exclusion principle - $(-1)^{n-1}P(\cap_i^n A_i)$
It seems that I shouldn't be including that if I want to have the correct answer...but surely I have to include it as I can't just drop an arbitrary term from some formula...so what am I missing?