One random subset contained in another

Two subsets $A$ and $B$ of a $5$-element set $X$ are chosen independently and uniformly from all $2^5$ subsets. What is the probability that $A\subseteq B$?

$\tfrac{243}{1024}$. Each element independently lands in one of four equally likely situations (in both, only $A$, only $B$, neither). $A\subseteq B$ rules out only “in $A$ but not $B$”, so the probability is $\left(\tfrac34\right)^5$.