1st part of my question:
I have that $P\left(\bigcup_{i=1}^{{2^n-n}}E_i\right)$ , how would I write it out using the inclusion-exclusion principle? I know it starts off: $\sum_{i=1}^{2^n-n} P(E_i)+...$ But after that Im not sure what goes next.
2nd part --- I also read somewhere that (by subadditivity), $P\left(\bigcup_{i=1}^{{2^n-n}}E_i\right) \le \sum_{i=1}^{2^n-n} P(E_i)$, but why is that the case? I dont understand how it by subadditivity the above inequality comes about.
Thanks.