Solving a Pedigree Between Heterozygous Half-Cousins

A man who is a known heterozygous carrier of oculocutaneous albinism marries his half-cousin (they share one common grandparent) as shown in the pedigree below. This trait is transmitted as a fully penetrant autosomal recessive. What is the probability that this couple will produce a child with this disorder?

A. 1/2
B. 1/4
C. 1/8
D. 1/16
E. 1/64

My calculation was 1/2 (for II-2 as he must be carrier) * 1/2 (for II-3) * 1/2 (for III-2) * 1/4 = 1/32. Please help me out by proper explanation to your steps and point out my mistakes. The correct answer given is 1/64. Pedigree shown in the image below.

• Also a proper attempt at answering for yourself should include your working, for example, why did you do 1/2 * 1/2 * 1/2 * 1/4 rather than 1/2 * 1/2 * 1/4 * 1/4? Therefore I think it should be closed as homework. Feb 5 '16 at 23:20

From what I can tell, you are not including the probability of the grandfather being a carrier (it could be the grandmother who is the carrier). Calculation should go like:

P(Child is born with disorder) = P(II-2 is carrier) * P(I-2 is carrier) * P(II-3 is carrier) * P(III-2 is carrier) * P(Child is homozygous recessive)

P(Child is born with disorder) = (1/2) * (1/2) * (1/2) * (1/2) * (1/4)

P(Child is born with disorder) = 1/64

• I was just about to comment, you can Google "A man who is a known heterozygous carrier of oculocutaneous albinism" and the question has been answered on other forums. For book questions I find this is often the fastest way to get an answer.
– CKM
Feb 5 '16 at 19:44
• thanks a lot everyone. but how do we get the probability of grandfather as he is the first one in the pedigree so how did u get his probability to be 1/2. please explain. @ CactusWoman Feb 6 '16 at 12:54
• @MaryamKhan The probably of the grandfather being the carrier is the same as the probability of the father being the carrier (given that the son is heterozygous). If we assume that the father is the carrier, we know that one of his parents must be the carrier. It must either be the father's mother or the father's father, giving us a 1/2 chance of the father's father being the carrier. The fact that the grandfather is the first in the pedigree does not really matter, as we calculate these probabilities up the lineage starting with the heterozygous man.
– C_Z_
Feb 6 '16 at 23:29
• Thanks a lot CactusWoman :-) now i understand it. Thanks a lot for your suggestion. that really helped when i searched the question on google @ Kendall Feb 8 '16 at 17:17