People with albinism have little pigment in their skin, hair, and eyes. The gene

Question

People with albinism have little pigment in their skin, hair, and eyes. The gene that governs albinism has two forms
(called alleles), which we denote a and A. Each person has a pair of these genes, one inherited from each parent. A
child inherits one of each parent's two alleles, independently with probability 0.5. Albinism is a recessive trait, so a
person is albino only if the inherited pair is aa.
a) Beth's parents are not albino but she has an albino brother. This implies that both of Beth's parents have type
Aa. Why?
b) Which of the types aa, Aa, AA could a child of Beth's parents have? What is the probability of each type?
c) Beth is not albino. What are the conditional probabilities for Beth's possible genetic types, given this fact?
d) Suppose that Beth marries Bob, who is albino (ie. his genetic type must be aa). What is the conditional
probability that a child of Beth and Bob is non-albino if Beth has type Aa? What is the conditional probability
of a non-albino child if Beth is type AA?

Explanation / Answer

(a) Beth's parents are not albino but she has an albino brother. This implies that both of Beth's
parents have type Aa.Why?                    
Ans:Because if Beth’s parents are not albino, but she has an albino brother (aa), then each parent must have the allele a

(b) Which of the types aa, Aa, AA could a child of Beth's parents have? What is the probability of each type?
Ans:Since each type is equally likely, and each is inherited independently of each other then
        P(AA) = 0.5(0.5) = 1/4 , P(Aa) = (0.5)(0.5) + (0.5)(0.5) = 1/2, and P(aa) = 1/4.

(c) Beth is not albino.What are the conditional probabilities for Beth's possible genetic types, given this fact?
Ans: we can rule out aa, since Beth is not an Albino. So having ruled out that possibility the new probabilities are:
                       P(AA | not aa) = 1/3.   P(Aa | not aa) = 2/3.

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