Product rule across STR loci — the odds a random stranger shares a DNA profile
A lab reads allele pairs at each STR marker.
STRs are short repeated DNA sequences.
Repeat counts vary widely between people.
Each locus sits at a known chromosome position.
PCR amplifies each targeted locus.
Capillary electrophoresis sorts fragments by size.
A genotype (two alleles) is called per locus.
CODIS uses 20 core loci plus a sex marker.
Each locus has its own population match frequency.
Population studies measure allele frequencies.
Genotype probability follows Hardy-Weinberg equilibrium.
Common alleles give higher match chances.
Loci sit on different chromosomes or far apart.
This makes their probabilities statistically independent.
Independence is what enables multiplication later.
Independence is the assumption the whole method relies on.
Independent locus probabilities multiply together.
For independent events, joint probability multiplies.
Each extra locus compounds the rarity.
Few loci already yield very small numbers.
More loci compared means lower combined probability.
Fewer loci leave more room for coincidence.
Modern kits use 20+ loci routinely.
Doubling loci roughly squares the rarity of the match.
One number now expresses the entire profile's rarity.
RMP answers one narrow question.
How likely is an unrelated match by chance.
It is not the chance of innocence.
Labs report RMP in scientific notation.
Jurors see phrases like "1 in a trillion."
Smaller RMP means stronger identification support.
A vanishing RMP does not by itself prove guilt.
Extremely low RMP values support confident identification.
Comparing RMP to world population clarifies scale.
Many profiles are rarer than the population itself.
This is why full profiles are so persuasive.
Relatives share more alleles than strangers.
Lab error rates matter more than tiny RMPs.
Database trawls need statistical correction.
RMP measures coincidence, not laboratory or relative risk.