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Dependent origination is not the same as determinism, and is not incompatible with the hypothesis that some things occur truly randomly.
You may take a look at the question about free will - Buddhism does not say there is no free will. Also the question about dependent origination and right effort may be of use - the following part of the accepted answer shown that it doesn't exclude the possibility of non-determinism:
When dependent origination is taught in the suttas, often what seems to be stressed are, literally, conditions, not causes as we often understand them (eg. agents that actively produce or directly contribute to a result)