Throughout this question, show your working and leave your answer in a clear from. Of those reporting to a medical clinic, 1% have medical condition Z. It is assumed that this figure of 1% is also the base rate across the population. There is a test for condition Z such that, for those patients who have condition Z, 90% will test positive; and for those patients who do not have condition Z, 20% will test positive.

(a) If a patient tests positive, what is the probability that the patient has condition Z?

i got answer : 9/207

is this correct?

After some consideration, it is decided that the test gives too many false positives, and it is decided to modify the test as follows. The new test is simply to administer the original test twice, where it is assumed that these two tests give results that are independent of one another. A patient will be considered to have tested positive on the new test precisely in those cases where both tests on the original test return a positive result. (b) If a patient has condition Z, what is the probability that the patient will test positive on the new test?

is this correct 0.81