Your friend has not been feeling well, and you made him go see a doctor. Doctor suspected he may have" Disease A". Disease A is present in about 5% of the population. The test designed to diagnose Disease A is 90% sensitive (i.e., the probability that the test is positive in the population of people with the disease is 90%), and 95% specific (i.e., the probability that the test is negative in the population of people without the disease is 95 %). Unfortunately, the test came back positive.

a) Given the positive test, what is the probability that your friend has the disease?

b) Given the positive test, is your friend more likely to have the disease than not to have it? Explain how the odds of disease have changed, from before the test to after the test.