Lavonne’s mother has brown eyes, and her father has blue eyes. Lavonne has brown eyes, and her husband has blue eyes. She knows that her children are equally likely to have brown or blue eyes. What is the probability that her first child will have blue eyes? If her first child has brown eyes, what is the probability that the second child will have blue eyes?

Let B = Brown (dominant) and b = blue (recessive)

Lavonne's genotype is Bb, because dad has bb.

Use Punnett square for Bb (Lavonne) and bb (husband)

https://www.google.com/search?client=safari&rls=en&q=punnett+square&ie=UTF-8&oe=UTF-8&gws_rd=ssl

Each birth is independent, so it does not effect subsequent births.

To solve these probability questions, we need to consider the principles of genetics relating to eye color inheritance.

Let's begin with the first question: What is the probability that Lavonne's first child will have blue eyes?

1. We know that Lavonne's mother has brown eyes, and her father has blue eyes.
2. Lavonne herself has brown eyes, which means she must have received one brown allele from her mother and one from her father.
3. Since Lavonne's husband has blue eyes, he must have received two blue alleles.
4. When determining the eye color of their child, both Lavonne and her husband will pass down one allele each.
5. The possible combinations of alleles for the child are:
a) Brown allele from Lavonne and blue allele from her husband.
b) Brown allele from Lavonne and brown allele from her husband.
6. Since we are interested in the probability of the child having blue eyes, we only need to calculate the probability of scenario a) happening.
7. The chance of each scenario happening is equal since Lavonne's children are equally likely to have brown or blue eyes.
8. Therefore, the probability that Lavonne's first child will have blue eyes is 1/2 or 0.5 (50%).

Moving on to the second question: If Lavonne's first child has brown eyes, what is the probability that the second child will have blue eyes?

1. We know that Lavonne's first child has brown eyes, which means they must have received one brown allele from Lavonne and one from her husband.
2. The possible combinations of alleles for Lavonne's second child are:
a) Brown allele from Lavonne and blue allele from her husband.
b) Brown allele from Lavonne and brown allele from her husband.
3. Since we are interested in the probability of the second child having blue eyes, we only need to calculate the probability of scenario a) happening.
4. The probability of scenario a) happening depends on the probability of Lavonne and her husband passing down specific alleles for their second child.
5. Given that Lavonne's first child has brown eyes, we already know the child has one brown allele.
6. Assuming the brown allele from Lavonne is equally likely to be passed on to the second child, the probability of this happening is 1/2 or 0.5 (50%).
7. Lavonne's husband, having blue eyes, can only pass down a blue allele since he has two blue alleles.
8. Therefore, the probability that Lavonne's second child will have blue eyes, given that the first child has brown eyes, is 1/2 or 0.5 (50%).

In summary:
- The probability that Lavonne's first child will have blue eyes is 1/2 or 0.5 (50%).
- If Lavonne's first child has brown eyes, the probability that the second child will have blue eyes is also 1/2 or 0.5 (50%).