# Biology Genetics- calculating probabilities

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#### Psyched101

##### New Member
7+ Year Member
I need some help understanding the answer to the following bio genetics question.

A woman is phenotypically normal but had a brother who had an autosomal recessive disorder that resulted in death during infancy. What is the probability that this woman is a carrier of the disorder that afflicted her brother?
a) 1/4
b) 1/3
c) 1/2
d) 2/3

I reasoned that for the brother to have the disease and the woman to be normal both parents had to be heterozygotes (I.e. Aa genotype). This means that there is a 25% chance for homozygous dominant offspring, 50% for heterozygous and 25% homozygous recessive. Since the woman is supposed to be a carrier she falls under the 50% category. Therefore I reasoned the answer is C. But it appears that the answer is D and the justification doesn't explain how they came to that answer.

Thanks in advance for the help!

I need some help understanding the answer to the following bio genetics question.

A woman is phenotypically normal but had a brother who had an autosomal recessive disorder that resulted in death during infancy. What is the probability that this woman is a carrier of the disorder that afflicted her brother?
a) 1/4
b) 1/3
c) 1/2
d) 2/3

I reasoned that for the brother to have the disease and the woman to be normal both parents had to be heterozygotes (I.e. Aa genotype). This means that there is a 25% chance for homozygous dominant offspring, 50% for heterozygous and 25% homozygous recessive. Since the woman is supposed to be a carrier she falls under the 50% category. Therefore I reasoned the answer is C. But it appears that the answer is D and the justification doesn't explain how they came to that answer.

Thanks in advance for the help!

What is the answer explanation? I am also confused why it is not 1/2 because her parents have to be heterozygous.

You have it right. Parents must have both been Aa, with the phenotypically abnormal infant aa.

Since this woman is phenotypically normal, she must be Aa. We know she isn't aa because she is phenotypically normal.

So total is AA, Aa, Aa, aa and she can't be aa - then 2/3 she is Aa a recessive carrier.

2 users
You have it right. Parents must have both been Aa, with the phenotypically abnormal infant aa.

Since this woman is phenotypically normal, she must be Aa. We know she isn't aa because she is phenotypically normal.

So total is AA, Aa, Aa, aa and she can't be aa - then 2/3 she is Aa a recessive carrier.

Thanks. I feel dumb haha

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Just to add onto what Cawolf said: There are 4 possible genetic scenarios, depending on which allele is inherited from mom or dad: AA, Aa, Aa, or aa. 4 possibilities, however, because aa is lethal and we're specifically being asked about carriers*, this reduces the probability to 3 possible genotypes. Of these 3, two are carriers for the recessive allele (since both of these are heterozygous genotypes), which is why the answer is 2/3.

*To be a carrier, you have to be living, which is why we exclude the lethal genotype all together in these probability questions.

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1 users
This is called conditional probability in stats. Given homo recessive dead and she will be alive, what is prob of rec carrier?
Geno outcome: AA 0.25, Aa 0.5, aa 0.25

Since you have 0.75 chance being alive and your chance of being simultaneously alive and carrier is 0.5. So 0.5/0.75=2/3

1 user
Just to add onto what Cawolf said: There are 4 possible genetic scenarios, depending on which allele is inherited from mom or dad: AA, Aa, Aa, or aa. 4 possibilities, however, because aa is lethal and we're specifically being asked about carriers*, this reduces the probability to 3 possible genotypes. Of these 3, two are carriers for the recessive allele (since both of these are heterozygous genotypes), which is why the answer is 2/3.

*To be a carrier, you have to be living, which is why we exclude the lethal genotype all together in these probability questions.

Your last point is an important distinction. Thanks

1 user
Ohh I see. So the probability isn't 2 in 4 (ie 1/2) it's 2 in 3! Makes sense! Thanks!!