3.61. Genes relating to albinism are denoted by A and a. Only those pcople who r

Question

3.61. Genes relating to albinism are denoted by A and a. Only those pcople who reccive the a gene from both par- ents will be albino. Persons having the gene pair A, a are normal in appearance and, because they can pass on the trait to their offspring, are called carriers. Suppose that a normal couple has two children, exactly one of whom is an albino. Suppose that the nonalbino child mates with a person who is known to be a carrier for albinism. (a) What is the probability that their first offspring is arn albino? (b) What is the conditional probability that their second offspring is an albino given that their firstborn is not?

Explanation / Answer

hre as one child is albino and both parent in normal appearance ; tehrefore both parent have Aa traits

hence nonalbino has probabiltiy of 1/3 of having AA trait and 2/3 of having Aa trait)

a)P(first offspring is albino)=P(nonalbiino child has AA trait and offspring is Albino)+P(nonalbiino child has Aa trait and offspring is Albino) =(1/3)*0+(2/3)*(1/4)=1/6

b)

P(firt offspring not Albino)=P(nonalbiino child has AA trait and offspring is not Albino)+P(nonalbiino child has Aa trait and offspring is not Albino)=(1/3)*1+(2/3)*(3/4)=5/6

hence P((nonalbiino child has AA trait|first offspring not albino)==(1/3)*1/(5/6)=2/5

P(nonalbiino child has Aa trait|first offspring not albino)=(2/3)*(3/4)/(5/6)=3/5

therefore P(second offspring is albino|first  offspring is not albino)

=P(nonalbiino child has AA trait|first offspring not albino)*P(second offspring is albino|nonalbiino child has AA trait)+P(nonalbiino child has a Aa trait|first offspring not albino)*P(second offspring is albino|nonalbiino child has Aa trait)

=(2/5)*0+(3/5)*(1/4)=3/20

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