Evaluation of twig queries over probabilistic XML is investigated. Projection is allowed and, in particular, a query may be Boolean. It is shown that for a well-known model of probabilistic XML, the evaluation of twigs with projection is tractable under data complexity (whereas in other probabilistic data models, projection is intractable). Under queryand-data complexity, the problem becomes intractable even without projection (and for rather simple twigs and data). In earlier work on probabilistic XML, answers are always complete. However, there is often a need to produce partial answers because XML data may have missing sub-elements and, furthermore, complete answers may be deemed irrelevant if their probabilities are too low. It is shown how to define a semantics that provides partial answers that are maximal with respect to a probability threshold, which is specified by the user. For this semantics, it is shown how to efficiently evaluate twigs, even under query-and-data complexit...