PYTHON PROGRAMMING CODE TO ASSERTAIN THESE:

person          genotype
mother                 ab
child                     bc
alleged father      de

X = P(man without C will contribute C)
X = P(contributed gene will mutate) * P(mutated gene will be a C)
m = observed rate of mutations/meiosis for the locus
P(mutated gene will be a C)  ie. Frequency of C allele  =  C
X =  C * m

For the numerator (X) Probability = 2ab x 2de x 0.5 x m x C

In order to explain this evidence the denominator must calculate the probability that the paternal allele is C and a random man would have a genotype inconsistent with paternity at this locus Y = P(paternal allele is C and random man has no C allele) = P(paternal gene is C) * P(random man has no C allele)

P(paternal allele will be a C)  ie. Frequency of C allele  =  C
P(random man has no C allele) = probability of exclusion
Y = C * A

For denominator (Y) Probability = 2ab x 2de x 0.5 x C x A

Hence the final result should be:

PI = X/Y
PI = (2ab * 2de * 0.5 * C * m ) / (2ab * 2de * 0.5 * C * A)
PI = m/A

N:B where PI is Paternity Index