Let’s go back to the cancer example. The prevalence of the disease in the population, 1 percent, is how we set our priors: prob(Hypothesis) = .01. The sensitivity of the test is the likelihood of getting a positive result given that the patient has the disease: prob(Data | Hypothesis) = .9. The marginal probability of a positive test result across the board is the sum of the probabilities of a hit for the sick patients (90 percent of the 1 percent, or .009) and of a false alarm for the healthy ones (9 percent of the 99 percent, or .0891), or .0981,
