Reverse-engineering gene identification. In Molecular Systems Biology (Vol. 3, 2007), geneticists at the University of Naples (Italy) used reverse engineering to identify genes. They calculated P1G0D2, where D is a gene expression data set of interest and G is a graphical identifier. Several graphical identifiers were investigated.

Suppose that, for two different graphical identifiers G1 and G2, P1D0G12 = .5 and P1D0G22 = .3. Also, P1D2 = .34, P1G12 = .2, and P1G22 = .8.

a. Use Bayes’s rule to find P1G1 0D2.

b. Use Bayes’s rule to find P1G2 0D2.