Mathematically, we write the observed frequency of Lifespan L among patients who voluntarily take the drug as P(L | D), which is the standard conditional probability used in statistical textbooks. This expression stands for the probability (P) of Lifespan L conditional on seeing the patient take Drug D. Note that P(L | D) may be totally different from P(L | do(D)). This difference between seeing and doing is fundamental and explains why we do not regard the falling barometer to be a cause of the coming storm. Seeing the barometer fall increases the probability of the storm, while forcing it to
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