1 and 2 are correct.
1 – Correct
30% work, at least some of the time, in the commercial sector. This covers doctor working in both sector together with the commercial sector alone. Thus some doctors must work in the public sector alone.
2 – Correct
2 is correct because 70% work solely in the public sector. On the other hand 30% work in either both or just commercial.
3 – Wrong
3 cannot be deduced as we do not know how much time doctors spend at each service.