miniPCR bio™ Electrophoresis Forensics Lab. Wrongfully Convicted? Instructor's and Student's Guide
Version: 1.1 - Release February 2022 - © 2022 by miniPCR bio™
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Probability and DNA profiles
Using the product rule in forensics
If you flip a coin once, there is a 50% chance that it will land heads up. In fact, any time you flip a
coin, the likelihood of getting a "heads" on that specific toss is 50% regardless of whether the
coin landed heads or tails on the previous tosses. We can calculate the probability of getting any
combination of heads and tails over a series of tosses using the product rule. The product rule
calculates the probability of a series of independent events by multiplying each event's probability.
For example, if you want to know the probability of getting 3 "heads" in a row, you multiply 0.5 x 0.5
x 0.5 to get 0.125 or 12.5%.
The product rule can also estimate the probability of a given STR profile in the human population
(Figure 1). Once forensic scientists have an STR profile with the genotypes for each STR location,
they can calculate the random match probability. The random match probability estimates the
frequency at which a given STR profile occurs in a population. This is a useful metric because it is
the same as the probability that a randomly selected person would share the genetic profile being
analyzed. To calculate the random match probability using the product rule, forensic scientists
multiply the frequency of each STR genotype in the profile (Figure 1). The genotype frequency
represents how prevalent the genotype is in the overall population.
STR location Genotype Genotype frequency
STR 1 7, 8 0.0054
STR 2 13, 13 0.0764
STR 3 11, 12 0.1772
Random match probability = genotype frequency STR 1 x genotype frequency STR 2 x genotype frequency STR 3
= 0.0054 x 0.0764 x 0.1772
= 7.31 x 10
-5
Figure 1. Calculating random match probability using the product rule
While you use the product rule for a series of coin tosses and STR profiles, STR genotypes are more
complicated than a coin flip because there are more than two alleles for each STR location. Further,
some STR alleles are quite common, while others are exceedingly rare. STR genotype frequencies
range from more than 20% to less than 0.00003%. That means some STR genotypes are so common
they are found in more than one in five people, whereas other genotypes are so rare they are found
in fewer than one in thirty million people!
