Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 39 / 3 / a / Solution

Only the copies inherited through the two related parents can share recent identity by descent; the other parental contributions come from unrelated founders in a pedigree. The related parents are full siblings. Their transmitted copies trace to the same shared grandparent with probability $1/2$, and then to the same copy of that grandparent with probability $1/2$. Thus the first-cousin identity-by-descent probabilities areTo compute the kinship coefficient, one random copy from each cousin selects those potentially shared contributions with probability $1/4$. Hence