A probability assignment on a finite set $X$ of Boolean variables gives each variable a rational probability in $[0, 1]$, the variables being independent: a valuation $\nu : X \to \{\bot, \top\}$ has probability $\Pr(\nu) = \prod_{\nu(x) = \top} \Pr(x) \cdot \prod_{\nu(x) = \bot} (1 - \Pr(x))$, and a Boolean function $f$ has probability $\Pr(f) = \sum_{\nu \models f} \Pr(\nu)$. A $\mathcal{B}[X]$-instance $\hat I$ is a probabilistic database: its random world under $\nu$ is the plain database of the tuples whose annotation holds at $\nu$. The marginal probability of a tuple $t$ in the answer of a query $q$ is $\sum_\nu \Pr(\nu) \cdot [t \in [\![q]\!]_{\hat I(\nu)}]$, and the annotation of $t$ in an annotated relation is the disjunction $\bigvee_{(t, \alpha)} \alpha$ of the annotations of its copies.