Probability of Union of 2 Events Always Equals 1? Just a curiosity on my end based on a homework problem that I am doing.
If $A,B$ are the only two events in the probability space, must it be true that: $P(A \cup B) = 1$?
Thanks.

A probability space is composed of a sigma-field of events.  The only sigma-field that contains only two events is $\mathscr{G} = \{ \varnothing, \Omega \}$.  So, this is the only time you will get only two events available in the probability space, in which case you have:
$$\begin{align}
\mathbb{P}(\varnothing) = \mathbb{P}( \Omega \cap \varnothing) &= 0, \\[6pt]
\mathbb{P}(\Omega) = \mathbb{P}( \Omega \cup \varnothing) &= 1. \\[6pt]
\end{align}$$
