4. (30 points) A classifier has portioned a set of 8 biomedical documents into C = { mentions the IL-2R a-promoter } (6 documents), and C (the rest). The gold standard indicates that only 3 documents actually mention the Interleukin-2 receptor alpha promoter (IL-2R a-promoter), and we determine that exactly one of them is (incorrectly) in C. In testing a post-processing heuristic, we select a document at random from C and move it in the class C. Next, we randomly select a document from C. a. What is the probability that the document we selected from C mentions the IL-2R a-promoter (according to the gold standard)? b. Next, we note that the document we selected from C does, in fact (according to the gold standard), mention the IL-2R a-promoter. Given this additional information, what is the probability that the document that we transferred from C to C mentioned (according to the gold standard) the IL-2R a-promoter (i.e., that we moved it to the wrong class)