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Genes relating to albinism are denoted by A and a. Only
Chapter 3, Problem 61P(choose chapter or problem)
Problem 61P
Genes relating to albinism are denoted by A and a. Only those people who receive the a gene from both parents 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 an albino?
(b) What is the conditional probability that their second offspring is an albino given that their firstborn is not?
Questions & Answers
QUESTION:
Problem 61P
Genes relating to albinism are denoted by A and a. Only those people who receive the a gene from both parents 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 an albino?
(b) What is the conditional probability that their second offspring is an albino given that their firstborn is not?
ANSWER:
Step 1 of 2
Given that genes relating to albinism are denoted by A and a. Only those people who receive the a gene from both parents will be albino.
a). To find the probability that their first offspring is an albino.
For the first offspring to be an albino, both parents would have to be carriers.
Then,
P(Offspring is aa) = P(offspring is aa/ both parents are Aa) P(both parents are Aa)
If both parents are Aa, then the probability is .
Then,
P(offspring is aa/ both parents are Aa) =
Now,
P(both parents are Aa) = P(other parent is Aa)
= P(other parent is Aa/other parent is normal)
= (by the definition)
Therefore,
P(offspring is aa) = P(offspring is aa/both parents are Aa) P(other parent is Aa)
Therefore, the probability that their first offspring is an albino is .