ok, so if I break it down even simpler, and forget the conditional:
Probability[rr + ar,
{rr \[Distributed] BernoulliDistribution[0.01],
ra \[Distributed] BernoulliDistribution[0.01],
ar \[Distributed] BernoulliDistribution[0.01],
aa \[Distributed] BernoulliDistribution[0.97]}]
why does that generate conditions? I guess I'm trying to find an idiomatic way, if possible, to use `Probability` for those types of a priori probability problems.