Appendix

Application of Bayes’s Rule

Bayes’s rule can be expressed as follows;

For the current problem, let’s use the notation that G refers to the prior probability that the suspect is guilty (before we know anything about the lab report) and E refers to the evidence of a blood match. We want to know P(G|E). Substituting in the above, we put in G for A and E for B to obtain:

To compute Bayes’s rule and solve for P(G | E), it may be helpful to use a table. The values here are the same as those used in the fourfold table here.

Then, rounding, P(Guilty | Evidence) = .10

         P(Innocent | Evidence) = .90