  Probabilities of causation play a crucial role in modern decision-making.
Pearl defined three binary probabilities of causation, the probability of
necessity and sufficiency (PNS), the probability of sufficiency (PS), and the
probability of necessity (PN). These probabilities were then bounded by Tian
and Pearl using a combination of experimental and observational data. However,
observational data are not always available in practice; in such a case, Tian
and Pearl's Theorem provided valid but less effective bounds using pure
experimental data. In this paper, we discuss the conditions that observational
data are worth considering to improve the quality of the bounds. More
specifically, we defined the expected improvement of the bounds by assuming the
observational distributions are uniformly distributed on their feasible
interval. We further applied the proposed theorems to the unit selection
problem defined by Li and Pearl.
