(a) 1 can be observed at the output if:
(i) 1 is produced at the source and transmitted correctly OR
(ii) 0 is produced at the source and is transmitted incorrectly.
So, Pr[1 at target] = Pr[1 at source]*Pr[transmitted correctly] + Pr[0 at source]*Pr[transmitted incorrectly]
(a) 1 can be observed at the output if: (i) 1 is produced at the source and transmitted correctly OR (ii) 0 is produced at the source and is transmitted incorrectly.
So, Pr[1 at target] = Pr[1 at source]*Pr[transmitted correctly] + Pr[0 at source]*Pr[transmitted incorrectly]
i.e Pr[1 at target] = 0.7*(1-0.2) + 0.3*0.2 = 0.56 + 0.06 = 0.62
(b) Straightforward use of Bayes theorem.