I faced a challenge leading me to ask this question:
If we have a set of n random variables, can we apply inclusion-exclusion for this set? Clearly, if we have a portfolio containing $X_{1}$, $X_{2}$, ..., $X_{n}$ that each shows a stock or bond price, and $A_{1}$, $A_{2}$, ..., $A_{n}$ are loss events of $X_{i}$s respectively, can I say that the probability of facing loss, on the whole of the portfolio, is $P\left(\bigcup_{i=1}^n A_i\right)$?
If yes, How can you justify the following condition:
The portfolio has two stocks $X_{1}$ and $X_{2}$ that are mutually exclusive (have strong negative correlation). $P(A_{1})$ and $P(A_{2})$ are greater than 0.5, so the probability of the portfolio's loss would be greater than $1$ since $P(A_{1}\cup A_{2})$ = $P(A_{1})$ + $P(A_{2}) \geq 1$.