Pedigrees, Prizes, and Prisoners: The Misuse of Conditional Probability

We present and discuss three examples of misapplication of the notion of conditional probability. In each example, we present the problem along with a published and/or well-known incorrect - but seemingly plausible - solution. We then give a careful treatment of the correct solution, in large part to show how careful application of basic probability rules can help students to spot and avoid these mistakes. With each example, we also hope to illustrate the importance of having students draw a tree diagram and/or a sample space for probability problems not involving data (i.e., where a contingency table might not be obviously applicable).