  Causal models are crucial for understanding complex systems and identifying
causal relationships among variables. Even though causal models are extremely
popular, conditional probability calculation of formulas involving
interventions pose significant challenges. In case of Causal Bayesian Networks
(CBNs), Pearl assumes autonomy of mechanisms that determine interventions to
calculate a range of probabilities. We show that by making simple yet often
realistic independence assumptions, it is possible to uniquely estimate the
probability of an interventional formula (including the well-studied notions of
probability of sufficiency and necessity). We discuss when these assumptions
are appropriate. Importantly, in many cases of interest, when the assumptions
are appropriate, these probability estimates can be evaluated using
observational data, which carries immense significance in scenarios where
conducting experiments is impractical or unfeasible.
