Question

People with albinism have little pigment in their skin, hair, and eyes. The gene that governs albinism has two forms (alleles), which are denoted by a and A. Each person has a pair of these genes, one inherited by 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 of the inherited pair is aa.

Hint: Make a probability tree.

1. Beth’s parents are not albino but she has an albino brother. What types must Beth’s parent’s be AA? Aa? aa?
2. Which of the types AA, Aa, aa, could a child of Beth’s parents have? What is the probability for each type?
3. Beth is not albino. What are the conditional probabilities for Beth’s possible genetic types?

Assume that the probabilities for Beth’s genetic types are given by part (c) above. Beth marries Bob who is albino.

4. What is the conditional probability that a child of Beth and Bob is non-albino if Beth is of type Aa?
5. What is the conditional probability that a child of Beth and Bob is non-albino if Beth is of type AA?
6. Beth and Bob’s first child is non-albino. What is the conditional probability that Beth is of type AA?

Answer 1

ANSWER::

(OR)

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.

      

	A	a
A	AA	Aa
a	aA	aa

(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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