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miniPCR bio™ Electrophoresis Forensics Lab. Wrongfully Convicted? Instructor's and Student's Guide Version: 1.1 - Release February 2022 - © 2022 by miniPCR bio™ Additional Supports P./26 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!