I need help understanding the following question. I believe the answer to be wrong.
Phenylketonuria is a rare autosomal recessive disorder with a carrier rate of 1/50 within Caucasian populations. A family enters a clinic with a sick child. Although neither parent is experiencing symptoms, you suspect PKU after a family history revels that the child’s paternal greatgrandmother had this condition. What are the chances, respectively, that the father is a carrier and that the child expresses this trait?
A. 100%, 1%
B. 50%, <1%
C. 50%, 1%
D. 25%, <1%
The answer states it is 50% with the following explanation:
B is correct. Since the child’s greatgrandmother had PKU, she must have possessed two copies of the recessive allele. She passed one of these alleles to her offspring (the father’s mother or father), making him or her an obligate carrier. This individual then had a 50% chance of passing it to the father of the sick child. (Note that we do not need to consider the father’s other parent in this calculation, as the carrier rate is extremely small.) Now, we know that the father had a 50% chance of inheriting one allele and thus has a 50% chance of giving it to his child. As we lack any specific information about the child’s mother, we can assume that she, like the population in general, runs a 1/50 risk of being a carrier. If so, she, too, has a 50% chance of giving her disease allele to the child. Multiplying these proportions yields (1/2)(1/2)(1/50)(1/2), or a 1/400 chance that the child is affected by PKU. A oneinfourhundred risk is less than 1%.
I disagree with this answer and explanation. If the father has a 50% of having the gene in heterozygous form, and then has a 50% change of passing the gene onto his daughter (making the obvious assumption that his wife has to have the heterozygous gene) then that means the offspring would have a 25% (1/2 x 1/2) chance of having the condition. How is it 50%?
Help on question

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Re: Help on question
Hey!
This question is a little tricky in how it is asked. In the last sentence of the question stem, "What are the chances, respectively, that the father is a carrier and that the child expresses this trait?" the key word is "respectively." So in the answer you are looking for the chance the father is a carrier and then the chance that the child expresses this trait. Looking at the answer choices you'll see they are all in the format: % #1, % #2.
Starting with the chance that the father is a carrier, we know that the child's paternal great grandmother (meaning father's grandmother) had the condition, so paternal great grandmother was homozygous recessive. This means that all of her children would be carriers, so one of the father's parents was definitely a carrier. This means he had a 50% chance of receiving a recessive allele from this parent and being a carrier. So this means choice B or C will be correct.
For the chance the child expresses the trait, this means that the child would need to get a recessive allele from mom AND dad. The father has a 50% chance of being a carrier and then a 50% chance of passing this recessive allele on, so for dad it is 1/2 x 1/2 = 1/4 (25% like you were thinking, but there is another step). The mother has no family history of the condition, so she has the general population chance of being a carrier, 1/50. Then there is a 50% chance of her passing on the recessive allele if she is a carrier, so for mom it is 1/50 x 1/2 = 1/100. Since you need both these events to happen, you multiply 1/4 x 1/100 to get a 1/400 chance that the baby has the condition (homozygous recessive), or a less than 1% chance, making choice B correct.
I hope this helps!
This question is a little tricky in how it is asked. In the last sentence of the question stem, "What are the chances, respectively, that the father is a carrier and that the child expresses this trait?" the key word is "respectively." So in the answer you are looking for the chance the father is a carrier and then the chance that the child expresses this trait. Looking at the answer choices you'll see they are all in the format: % #1, % #2.
Starting with the chance that the father is a carrier, we know that the child's paternal great grandmother (meaning father's grandmother) had the condition, so paternal great grandmother was homozygous recessive. This means that all of her children would be carriers, so one of the father's parents was definitely a carrier. This means he had a 50% chance of receiving a recessive allele from this parent and being a carrier. So this means choice B or C will be correct.
For the chance the child expresses the trait, this means that the child would need to get a recessive allele from mom AND dad. The father has a 50% chance of being a carrier and then a 50% chance of passing this recessive allele on, so for dad it is 1/2 x 1/2 = 1/4 (25% like you were thinking, but there is another step). The mother has no family history of the condition, so she has the general population chance of being a carrier, 1/50. Then there is a 50% chance of her passing on the recessive allele if she is a carrier, so for mom it is 1/50 x 1/2 = 1/100. Since you need both these events to happen, you multiply 1/4 x 1/100 to get a 1/400 chance that the baby has the condition (homozygous recessive), or a less than 1% chance, making choice B correct.
I hope this helps!
Re: Help on question
Thank you!!