Genetics: What is the probability that the third child will be affected

[TytoAlba95]

Homework Statement

About 1% individuals in a population suffer from a genetic disorder. The cause was traced to such individuals being homozygous recessive for a single locus with two alleles. The elder of the two children of a family(where both the parents are normal) suffers from the disorder, while the younger one is normal. What is the probability that the third child will be a normal daughter?
(a) 49.5%
(b)12.5%
(c)37.5%
(d)25%

Relevant Equations

Ans: (c)

pg-363, sum-334

Attempt:

The disorder is autosomal recessive.
The probability = Probability of being a daughter x Probability of an affected child being born = ½×¼ = 1/8 x100 =12.5%

 

[PeroK]

Problem Statement: About 1% individuals in a population suffer from a genetic disorder. The cause was traced to such individuals being homozygous recessive for a single locus with two alleles. The elder of the two children of a family(where both the parents are normal) suffers from the disorder, while the younger one is normal. What is the probability that the third child will be a normal daughter?
(a) 49.5%
(b)12.5%
(c)37.5%
(d)25%
Relevant Equations: Ans: (c)

pg-363, sum-334

Attempt:

The disorder is autosomal recessive.
The probability = Probability of being a daughter x Probability of an affected child being born = ½×¼ = 1/8 x100 =12.5%

It looks like you've calculated the probability of an affected daughter.

 

[TytoAlba95]

It looks like you've calculated the probability of an affected daughter.

Oh! My bad.
P= ½×¾ x 100=37.5%

Thanks :)

 

[Buzz Bloom]

I looked at this thread out of curiosity, and I find myself confused.

Since the first child has the disorder, and both parents do not, this means each parent carries the bad allele on just one of the two chromosomes which are home to the relevant gene. For a third child to not have the disorder, means the child must avoid receiving the bad allele from both parents. A child will get the bad allele from the mother half the time, and from the father half the time, and from both (1/2)*(1/2) = 1/4 the time. Thus the third child avoids inheriting the bad allele form both parents 1-(1/4) = 3/4 of the time. What really confuses me is that 75% is not listed among the four answer choices.

 

[TytoAlba95]

I looked at this thread out of curiosity...

Thanks.

What really confuses me is that 75% is not listed among the four answer choices.

''What is the probability that the third child will be a normal daughter?''

Actually, the question is about a normal daughter, so its ½ × ¾.

 

[Buzz Bloom]

Actually, the question is about a normal daughter, so its ½ × ¾.

Hi Sanjukta:

Thanks for the correction. One of these days I will regain my ability to read accurately.

Regards,
Buzz

 

[pinball1970]

Hi Sanjukta:

Thanks for the correction. One of these days I will regain my ability to read accurately.

Regards,
Buzz

Me too. I saw the answer and thought what?? Then I re-read the op.