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\begin{abstract}
In this work, we study the problem of computing a tuple's expected multiplicity over probabilistic databases with bag semantics (where each tuple is associated with a multiplicity) exactly and approximately.
We consider bag-\abbrTIDB\xplural where we have a bound $\bound$ on the maximum multiplicity of each tuple and tuples are independent probabilistic events (we refer to such databases as \abbrCTIDB\xplural).
We are specifically interested in the fine-grained complexity of computing expected multiplicities and how it compares to the complexity of deterministic query evaluation algorithms --- if these complexities are comparable, it opens the door to practical deployment of probabilistic databases.
  Unfortunately, our results imply that computing expected multiplicities for \abbrCTIDB\xplural based on the results produced by such query evaluation algorithms introduces super-linear overhead (under parameterized complexity hardness assumptions/conjectures).
  We proceed to study approximation of expected result tuple multiplicities for positive relational algebra queries ($\raPlus$) over \abbrCTIDB\xplural and for a non-trivial subclass of block-independent databases (\abbrBIDB\xplural).
  We develop a sampling algorithm that computes a $(1 \pm \epsilon)$-approximation of the expected multiplicity of an output tuple in time linear in the runtime of the corresponding deterministic query for any $\raPlus$ query.
\end{abstract}

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