  The probabilities of causation are commonly used to solve decision-making
problems. Tian and Pearl derived sharp bounds for the probability of necessity
and sufficiency (PNS), the probability of sufficiency (PS), and the probability
of necessity (PN) using experimental and observational data. The assumption is
that one is in possession of a large enough sample to permit an accurate
estimation of the experimental and observational distributions. In this study,
we present a method for determining the sample size needed for such estimation,
when a given confidence interval (CI) is specified. We further show by
simulation that the proposed sample size delivered stable estimations of the
bounds of PNS.
