Product rule (probability)
Definition
The rule that P(A and B) = P(A) x P(B) holds only when A and B are independent. Applying it to correlated events produces probabilities that are far smaller than the true values, making a coincidence appear impossibly rare.
Related terms
- Defence fallacy
- The converse error of inflating the importance of the RMP by arguing that, because many people in the population share the profile,...
- Likelihood ratio (LR)
- The ratio of two conditional probabilities: the probability of the observed evidence given the prosecution's hypothesis (same source), divided by the probability...
- Prosecutor's fallacy
- The error of treating the RMP (or its reciprocal) as the probability that the defendant is innocent, or as the probability that...
- Reference class
- The population against which a probability or frequency is calculated. Choosing the wrong reference class, for example using general population allele frequencies...
- Transposition of the conditional
- The mathematical name for the error at the core of the prosecutor's fallacy. P(A | B) and P(B | A) are generally...
Explained in
- History of Statistical Evidence in CourtsThe rule that P(A and B) = P(A) x P(B) holds only when A and B are independent. Applying it to correlated events produces probabilities that are far smaller th...