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Random Match Probability Product Rule Calculator

Run the Random Match Probability Calculator Fullscreen

About This MicroSim

When a DNA profile from a crime scene matches a suspect, the key question is: how likely is it that a random, unrelated person would match by chance? That number is the random match probability (RMP), and it is what makes DNA evidence so powerful in court.

The RMP is calculated with the product rule. Because the STR loci used in DNA profiling are inherited independently, you can multiply the population frequency of the genotype at each locus together. Each locus on its own is not that rare — but multiply five, six, or eight of them and the probability becomes astronomically small.

This MicroSim lets you build that product yourself, one locus at a time, and watch the probability plunge below the entire world population.

How to Use It

  1. The table lists eight STR loci, each with a genotype and its population frequency. All start checked.
  2. Uncheck and recheck loci to add or remove them from the product. The Running Product curve (log scale) drops a step lower with every locus you add.
  3. Press Calculate Product to reveal the RMP in scientific notation and as "1 in X".
  4. Read the How rare is that? bars: they compare your 1-in-X value against the U.S. population and the world population on a log scale.
  5. Use Select All or Clear to jump between the full profile and an empty one.

What You Can Learn

  • Apply the product rule to calculate a multi-locus random match probability.
  • Express an RMP both in scientific notation and as a "1 in X" odds statement.
  • Explain why adding loci shrinks the probability exponentially, and judge when a profile is rare enough to point to one person.

You can embed this MicroSim on your own web page with this iframe:

<iframe src="https://dmccreary.github.io/forensic-science/sims/rmp-product-rule/main.html"
        width="100%" height="552" scrolling="no"></iframe>

Lesson Plan

Audience: High-school forensic science (grades 9–12) Time: 10–15 minutes Bloom level: Apply (L3) — calculate.

Worked example. Clear all loci, then check them back one at a time. Read the running product aloud after each: ~1 in 17, then 1 in 300, then 1 in 8,600… By the eighth locus it is 1 in tens of billions — rarer than every person on Earth.

Guided questions:

  • A single locus has a genotype frequency of 0.06 — about 1 in 17 people. Why isn't that enough to identify someone, but eight such loci are?
  • What does the product rule assume about the loci, and why does that assumption matter?
  • At how many loci does your RMP first drop below the U.S. population? Below the world population?

Extension. Standard CODIS profiling uses 20 loci. Using the pattern you see here, explain why the RMP for a full 20-locus profile is often quoted as rarer than 1 in a quadrillion, and why analysts still report it as a probability rather than a certainty.

References

Specification

This MicroSim was generated from a specification in Chapter 8: Forensic DNA Profiling.

Design note: the loci and frequencies are realistic teaching values, not a specific population database, and the product rule here assumes the loci are independent (as the standard model does). Real casework adjusts for population substructure and relatedness, so the calculated RMP is an instructional estimate rather than a courtroom figure.