# Table 5 Conditional probabilities of mating type and child genotype

Mating type = i Pr(Mating type = i|D, pop = k) Child genotype Notation Pr(Child genotype|D, Mating type = i, pop = k) (t= 1/2 when k= 2) Pr(x abc |D, pop = k)
MM × MM (i = 1) μ k,1 MM x 222 1 μ k,1
MM × MNC(i = 2) μ k,2 MM x 212 t μ k,2 t
MM × MNC(i = 2) μ k,2 MN x 211 (1 - t) μk,2(1 - t)
MM × NN(i = 3) μ k,3 MN x 201 1 μ k,3
MN × MN(i = 4) μ k,4 MM x 112 t 2 μ k,4 t 2
MN × MN(i = 4) μ k,4 MN x 111 2t(1 - t) 2 μk, 4t(1 - t)
MN × MN(i = 4) μ k,4 NN x 110 (1 - t)2 μk,4(1 - t)2
MN × NN(i = 5) μ k,5 MN x 101 t μ k,5 t
MN × NN(i = 5) μ k,5 NN x 100 (1 - t) μ k,5 (1 - t)
NN × NN(i = 6) μ k,6 NN x 000 1 μ k, 6
1. In this table, the high risk allele is M. Also, we define D to be the event that the child is affected. Note that 1 ≤ k ≤ 2. The last column is computed using the definition of conditional probability. Schaid and Sommer  also demonstrated this calculation. Note that $\text{Pr}\left({x}_{abc}|D,\text{pop}=k\right)={f}_{B}\left({x}_{abc};{\stackrel{\to }{\theta }}_{k}\right)$. Finally, t = Pr(heterozygous parent transmits an M allele to an affected child). 