Give the Bayes formula for two events and for multivalued random variables. Solve the following problem: Assume that you are in the UK. You go to see a doctor about a minor abdominal pain. The doctor selects you (at random) to have the test for a new ABCvirus, which for the purposes of this exercise we will say is currently suspected to affect 1 in 10,000 people in the UK. The test is 98% accurate, in the sense that the probability of a false positive is 1% and the probability of a false negative is also 1%. You test positive. Estimate the probability that you have the ABCvirus.