## DNA Forensics Problem Set 1

### Problem 6: Probability

Probability calculations are used in forensic applications of DNA fingerprinting to determine if:

### Tutorial

The frequency of an allele pattern at a single VNTR locus
 The frequency of the occurrence of different VNTR alleles in many different populations of racially and ethnically diverse peoples have been determined. The chance that an individual might have a particular pattern of 2 VNTR alleles is given by the expression 2pq, where p and q are the frequencies of the two alleles in the reference population. If p is 0.1 (10% of the reference population) and q is 0.05 (5% of the reference population, then the frequency of the DNA profile is 0.01 (or 1% of the reference population).
The frequency of a 5-locus DNA Profile.
 Imagine that a DNA forensic scientist determined that DNA from semen from a vaginal swab of a rape victim matched the DNA profile of a suspect at 5 different VNTR loci. Assume that the frequency of the DNA profiles for the 5 individual loci were 0.01, 0.02, 0.06, 0.10, and 0.03. How common or rare would this 5 locus DNA profile be in the reference population? In most cases, a "product rule" calculation can be done by multiplying each individual probability together. Thus the frequency of the profile is 0.01 x 0.02 x 0.06 x 0.10 x 0.03 = 3.6 x 108. Another way to express this probability is take the reciprocal of this number, 1/3.6 x 108 = 27.8 million. The DNA analyst could report that the DNA profile that is shared by the suspect and the evidence might occur by chance in 1 person out of 27.8 million. The jury could use this information to evaluate whether the match of DNAs might have occurred by chance.

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University of Arizona
Tuesday, August 20, 1996
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