(Assuming that two tests are independent, which is a rather unrealistic assumption in this case) If you know how to calculate the ~30% answer to the first part of the question, then this problem is pretty straightforward to solve. Just use Bayes' rule again, treating the posterior from your first calculation (~30%) as your prior for the next calculation.

If Kim came from a population that had a ~30% prior of having cancer and took one test which came out negative, then her probability after that one test would be the same as Jane's probability after both tests.