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?

Question

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?

Answer 1

prob(blue) = prob(brown) = 1/2

a) so prob(first child brown) = 1/2

since these prob's are independent, that is, just because the first child has brown eyes, does not mean the second is more likely to have blue eyes

so prob(2nd have blue) = 1/2

Answer 2

To answer this question, we can use the principles of genetics to determine the probability of the children inheriting certain eye colors.

Let's break down the problem step by step:

1. Lavonne has brown eyes, and her mother also has brown eyes. This means that Lavonne has at least one dominant brown eye gene.

2. Lavonne's father has blue eyes, which means he has two recessive blue eye genes.

3. When Lavonne and her husband have children, they each have one brown gene (dominant) and one blue gene (recessive) to pass on to their children. Therefore, the probabilities for each child are as follows:
- 50% chance of inheriting the brown gene from Lavonne and the blue gene from her husband, resulting in brown eyes.
- 50% chance of inheriting the blue gene from Lavonne and the blue gene from her husband, resulting in blue eyes.

Now, let's answer the specific questions:

1. What is the probability that her first child will have blue eyes?
Since there is a 50% chance for each child to have blue eyes, the same probability applies to the first child as well. Therefore, the probability that the first child will have blue eyes is 50%.

2. If her first child has brown eyes, what is the probability that the second child will have blue eyes?
If the first child has brown eyes, it means they have inherited the brown gene from Lavonne along with the blue gene from her husband. Therefore, the probability of the second child having blue eyes remains the same as before: 50%.

In conclusion:
- The probability that Lavonne's first child will have blue eyes is 50%.
- If the first child has brown eyes, the probability that the second child will have blue eyes is also 50%.