Multiplication Rule
Definition
For any two events: P(A and B) = P(A) x P(B|A). When A and B are independent, this simplifies to P(A) x P(B). The simple product form is only valid under confirmed independence.
- General formula
- P(A and B) = P(A) x P(B|A)
- Independent-event form
- P(A) x P(B)
- Field
- Probability theory
- Caution
- Product form valid only under confirmed independence
Common questions
What forensic mistake does misapplying the independent-event form cause?+
Multiplying individual match probabilities as if they were independent when the underlying events are correlated, for example combined trait frequencies within relatives, overstates rarity and produces an artificially small, misleading combined probability.
How does an analyst confirm two events are independent before using the simplified rule?+
Independence has to be established through the underlying biology or process generating the events, such as validated population genetics for unrelated STR loci, rather than assumed for convenience, since assuming it wrongly is a recognised statistical fallacy in court testimony.
Related terms
- Conditional Probability
- The probability of event A given that event B has already occurred, written P(A|B). Conditional probability is the basis of the multiplication...
- Hardy-Weinberg Equilibrium
- A condition in a population where genotype frequencies at a single locus conform to expectations derived from allele frequencies alone, assuming random...
- Linkage Disequilibrium
- The non-random association of alleles at different loci within a population. Certain HLA allele combinations (e.g., HLA-A1 with HLA-B8 with HLA-DR3) occur...
- Positive Dependence
- Events are positively dependent when the occurrence of one increases the probability of the other: P(A|B) > P(A). In this case P(A...
- Statistical Independence
- Events A and B are independent if P(A|B) = P(A), equivalently P(A and B) = P(A) x P(B). Knowing B occurred gives...