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(xabc|D, pop = k)
MM × MM (i = 1)	μk,1	MM	x222	1	μk,1
MM × MNC(i = 2)	μk,2	MM	x212	t	μk,2 t
MM × MNC(i = 2)	μk,2	MN	x211	(1 - t)	μk,2 (1 - t)
MM × NN(i = 3)	μk,3	MN	x201	1	μk,3
MN × MN(i = 4)	μk,4	MM	x112	t2	μk,4 t2
MN × MN(i = 4)	μk,4	MN	x111	2t(1 - t)	2 μk,4 t(1 - t)
MN × MN(i = 4)	μk,4	NN	x110	(1 - t)2	μk,4(1 - t)2
MN × NN(i = 5)	μk,5	MN	x101	t	μk,5 t
MN × NN(i = 5)	μk,5	NN	x100	(1 - t)	μk,5 (1 - t)
NN × NN(i = 6)	μk,6	NN	x000	1	μk,6

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 [63] also demonstrated this calculation. Note that $\text{Pr}\left(x_{abc}|D,\text{pop}=k\right)=f_B\left(x_{abc};{\overrightarrow{\theta }}_k\right)$. Finally, t = Pr(heterozygous parent transmits an M allele to an affected child).