A study of swab test for COVID-19 in the United Kingdom found that they had a false negative rate between 2 and 33%. This is in part because the test is more sensitive a certain time after infection. The false positive rate was between 0.8 and 4%. For the purposes of this problem, let's assume that the false negative rate is 15% and the false positive rate is 2%. The current positivity rate in NYC is 6%which gives us an estimate of the prevalence (fraction of NYC residents with COVID). a) Imagine that a NYC resident takes the swab test used in the UK and the test comes back positive. What is the probability that they have COVID-19? b) Imagine that a NYC resident takes the swab test used in the UK and the test comes back positive. What is the probability that they do not have COVID-19? c) Imagine that a NYC resident takes the swab test used in the UK and the test comes back negative. What is the probability that they do not have COVID-19? d) Imagine that a NYC resident takes the swab test used in the UK and the test comes back negative. What is the probability that they have COVID-19?