arginemia is a autosomal reseive disease. cowden syndrom is a autosomal dominant

Question

arginemia is a autosomal reseive disease. cowden syndrom is a autosomal dominant disease.

a normal man mates a woman who has cowden syndrome. they have two children: a daughter with arginemia and a son with cowden. the son mates witn a woman who has a homozygous recessive genotype for both genes. what is the probability that they will have a daugter with both arginemia and cowden?

so the answer is 1/12th.

this is what I understood from the answer solution.

lets call Cc or CC = cowden

cc= normal, no cowden

aa= arginemia

Aa or AA= normal, no argenima

first generation: woman is Aa/Cc and man is Aa/cc -> daughter is aa/cc and son is Aa/Cc

son mates a double recessive -> daughter is aa/Cc

the solution says that the father of the daughter we are trying to find the probability for is Aa or AA. but since we know that the daughter will be aa and the wife/mom is aacc we know the father has to be Aa

P(father is Aa) = 2/3

then we have to take into account since the gamete for the father is Aa there is a 50% probability he will hass a A allele and 50% to pass a a allele

the overall probability of having arginemia is 2/3 * 1/2 = 1/3

I understood uptill here but I am confused about calculating the probability of having cowden syndrome.

the solution says that the overall probability of having cowden syndrom is 1/2 which I understand but why didn't the solution take into account that there is a 50% chance the father passes a C allele and a 50 % chance that the father passes a c allele? I throught this part would be 1/2 * 1/2 = 1/4 ???

Explanation / Answer

Cowden is an autosomal dominant disease. The question says that normal man mates with woman having cowden disease. So, the genotype of normal man should be cc and genotype of woman could be either CC or Cc. The overall probability of having cowden syndrome is 1/2 because normal man will transmit only c gene and only woman will transmit C gene. This can be easily understood using Punnett square.

Man (cc) X Woman (Cc)

1/2 offsprings will have Cc genotype and 1/2 will have cc genotype.

So,the overall probability of having Cowden syndrome is 1/2

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