Conditional probability: Medical tests and risk of disease

Students can experiment with different scenarios by substituting their own values for prevalence of disease, and true positive, and false positive rates of the medical test.
What factors matter for the likelihood of having a disease, given that the test is positive? For what values will the likelihood of disease given a positive test result be greater than 0.50? Why, do you think, do most people get the question wrong if we simply ask them to estimate the risk of infection given that the test result is positive?