disease a occurs with probability 0.1 (i.e. it is present in 20% of the population), and disease b occurs with probability 0.2. it is not possible to have both diseases. you have a single test. this test reports positive with probability 0.8 for a patient with disease a, with probability 0.5 for a patient with disease b, and with probability 0.01 for a patient with no disease. what is the posterior probability you have either disease, or neither, if the test comes back positive?