Gene expression profiling is a state-of-the-art method for determining the biology of cells. In Briefings in Functional Genomics and Proteomics (Dec. 2006), biologists reviewed several gene expression profiling methods. The biologists applied two of the methods (A and B) to data collected on proteins in human mammary cells. The probability that the protein is cross-referenced (i.e., identified) by method A is .41, the probability that the protein is cross-referenced by method B is .42, and the probability that the protein is cross-referenced by both methods is .40.
a. Draw a Venn diagram to illustrate the results of the gene-profiling analysis.
b. Find the probability that the protein is cross-referenced by either method A or method B.
c. On the basis of your answer to part b, find the probability that the protein is not cross-referenced by either method?