Probabilistic choice and demonic nondeterminism have been combined in a
model for sequential programs [11, 8] in which program renement is dened
by removing demonic nondeterminism. Here we study the more general topic
of data renement in the probabilistic setting, extending standard techniques
to probabilistic programs. We use the method to obtain a quantitative assessment
of safety of a (probabilistic) version of the steam boiler [1]