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# Probability of Exclusion

The probability of exclusion provides an estimate of the proportion of the population that has a genotype composed of at least one allele not observed in the mixed profile.12,13 This approach, for practical purposes, is considered conservative and analysts do not need to make assumptions about the mixture or number of contributors. It has, however, been criticized because it does not make use of all of the available genetic data.12

The steps for applying the probability of exclusions (PE) are to sum all of the homozygotes and to sum all the heterozygotes that are represented within the mixed profile.

For a given locus, assuming Hardy-Weinberg equilibrium,

PE locus = 1-p2

Or if Hardy-Weinberg equilibrium is not assumed,

PE locus = 1-p2 - θp(1-p)

The probability of exclusion (PE) is calculated for each homozygous locus by repeating the above steps, performing the equivalent calculation for heterozygotes, and summing the calculated values.

Total Probability of Exclusion without Theta

PE = 1 - (p1 + p2 + ... + pn)2

PEmix = plocus(1) + plocus(2)+ ... + plocus(n)

Total Probability of Exclusion with Theta

PE = 1 - (p1 + p2 + ... + pn)2 - θ[p1(1-p1) + p2(1-p2) + ... + pn(1-pn)]

PEmix = plocus(1) + plocus(2)+ ... + plocus(n)