Question

The color of a person's eyes is determined by a single pair ofgenes. If they are both blue-eyed genes, then the person will haveblue eyes; if they are both brown-eyed genes, then the person willhave brown eyes; and if one of them is a blue-eyed gene and theother a brown-eyed gene, then the person will have brown eyes.(Because of the latter fact, we say that te brown-eyed gene isdominant over the blue-eyed gene.) A newborn child independentlyreceives one eye gene from each of its parents, and the gene itreceives from a parent is equally likely to be either of the twoeye genes of that parent. Suppose that Smith and bot of his parentshave brown eyes, but Smith's sister has blue eyes.What is the probability that Smith possesses a blue-eyedgene?Suppose that Smith's wife has blue eyes. What is theprobability that their first child will have blue eyes?If their first child has brown eyes, what is the probabilitythat their next child will also have brown eyes?

Answer 1

Suppose that Smith and bot of his parents have brown eyes (B),

Here, you could have two choices for both parents, BB or Bb

BBxBB = 100% BB all children will have brown eyes.

BBxBb = 50% BB 50% BB all children will have brown eyes.

BbxBb= 25% BB 50% Bb 25% bb 75% of children will have brown eyes, 25% of children will have blue eyes.

but Smith's sister has blue eyes (b).

This means both parents have to be heterozygous dominant Bb

What is the probability that Smith possesses a blue-eyed gene?

If we go back to the offspring probabilities, you have 50% chances of Smith to have the blue-eyed gene.

Suppose that Smith's wife has blue eyes.

The only chance here is that she has bb genes.

What is the probability that their first child will have blue eyes?

If Smith has the blue eye gen the probabilities are

Bbxbb= 50% Bb 50% bb

This means they have a 50% chance of having a blue-eyed child.

If their first child has brown eyes, what is the probability that their next child will also have brown eyes?

Still, 50% because probabilities are always the same in each pregnancy.