The causal impact of tar on cancer is: P(cancer|do(tar)) - P(cancer|do(no tar)) where, P(cancer|do(tar)) = P(cancer|tar,smoking) * P(smoking) + P(cancer|tar,no smoking) * P(no smoking) P(cancer|do(no tar)) = P(cancer|no tar,smoking) * P(smoking) + P(cancer|no tar,no smoking) * P(no smoking)