meed help plz

Froblem 4: Diagnostic Tests and Bayes' Rule I have decided to get myself tested for COVID-19 antibodies. However, being comfortable with statistics, I am curious about what the test means for my actual status. Let's investigate these questions, showing all your work. a) The antibody test I take has a sensitivity (a.k.a. true positive rate) of 97.5% and a specificity (a.k.a. true negative rate) of 99.1%. If you are not familiar with sensitivity vs specificity, please see Wikipedia. Assume that 4% of the population actually have COVID-19 antibodies. Write down the joint probability distribution P(S,R) with events for antibody state S{ true, false } and test result R{ true, false }. b) Assuming I receive a positive test result, use Bayes' rule to calculate the probability that I actually have COVID-19 antibodies. c) Assuming I receive a negative test result, what is the probability that I do not have COVID-19 antibodies? d) Assume I take the test twice, and receive a positive result in the first test and a negative result in the second test. Assume that the two test results are conditionally independent given the existence of the antibody. What is the probability that I have COVID-19 antibodies according to Bayes' rule? e) Now assume that only 1% of the population has COVID-19 antibodies. Repeat parts (b) and (c) with this revised prior belief