2. In pooled or batch testing, samples are combined and a single result is obtained (positive or negative for the pooled sample). If the pooled testing were to work perfectly, then a positive test would mean at least one person in the pool is infected with SARS-CoV-2, and a negative test would mean nobody in the pool is infected. Of course, the tests do not work perfectly, and there can be false positives and false negatives. Let's look at a simplified example. Suppose again that in a certain region, 0.2% of people with no symptoms and no known exposure carry SARS-CoV-2. 100 people without symptoms and no known exposure are randomly selected from this region and pool tested. Suppose under these conditions, the pooled test will give a false negative with probability 0.20 and a false positive with probability 0.01. (If at least one person in the pool has SARS-CoV-2 the test will come back positive with probability 0.80, and if nobody is infected the test will be positive with a probability of 0.01. While in reality, the false negative rate likely depends somewhat on the number of positive individuals, let's ignore that complication here.) Tom is in the pool of 100 randomly selected people. The pooled test has come back positive. What is the probability that Tom is infected with SARS-CoV-2? Show your work