" Assuming Hardy-Weinberg equilibrium, SNPs with minor allelic frequency between 0.4 and 0.5 would be found homozygous in two people 23% to 25% of the time for both alleles. The probability of both donor and recipient having a different allele is therefore 11.5% to 12.5% using accepted estimation models for calculation of exclusion probabilities" This is from an article I'm reading. I do not follow how they got their number. Can someone explain? Thanks!
Assuming you are familiar with Hardy-Weinberg (which to me is simply binomial opening of (a+b)^n), the first part calculates the probabilty of being homozygous for a allele of let's say frequency 0.5. Then, the change of having both alleles the same would be 0.5*0.5 = 0.25. If the frequency would be 0.4 than it would be 0.4*0.4 = 0.16.
Next it calculates what are the chances that 2 people are having different alleles. Here I assume they calculate the probablity of both being homozygous for different alleles. Than, if you take the number above, 0.25 which is probability of being homozygous for 1 allele, than consider the other person begin homozygous for the other allele, which is again 0.25. So this situation occurs if:
person a is homozygous for alele 1 and the other person is homoozygous for allele 2: 0.25*0.25 = 0.0625
OR vice versa : 0.0625
add them up 0.125.
This is all I could understand based on this passage,
I hope it helps.