ABSTRACT
In this chapter, the authors explain a paradox about conditional probability and aggregation of data. Conditional probability is essential for scientific, medical, and legal reasoning, since it shows how to incorporate evidence into their understanding of the world in a logical, coherent manner. The law of total probability relates conditional probability to unconditional probability. It is essential for fulfilling the promise that conditional probability can be used to decompose complicated probability problems into simpler pieces, and it is often used in tandem with Bayes’ rule. Most people find it surprising to learn that the conditional probability of having the disease given a positive test result is only 16%, even though the test is 95% accurate. The outcry over the misuse of conditional probability in the Sally Clark case led to the review of hundreds of other cases where similar faulty logic was used by the prosecution.
