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

######Math Alert########################
Since no backdoor between smoking and tar:

P(tar|do(smoking)) = P(tar|smoking) 
& 
P(no tar|do(smoking)) = P(no Tar|smoking)

And from back door adjustment for tar and cancer:

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)

Finally,
P(cancer|do(smoking)) = (P(cancer|tar,smoking) * P(smoking) + 
                        P(cancer|tar,no smoking) * P(no smoking))
                        * P(tar|smoking) 
                        +
                        (P(cancer|no tar,smoking) * P(smoking) + 
                        P(cancer|no tar,no smoking) * P(no smoking))
                        * P(no tar|smoking)