Question

A husband and wife have normal vision, although both of their fathers are red- green color-blind, inherited as an X-linked recessive condition. What is the probability that their first child will be (a) a normal son, (b) a normal daughter, (c) a color-blind son, (d) a color-blind daughter?

Short answer

Answer: The probabilities for their first child are as follows: - Normal son: 25% - Normal daughter: 25% - Color-blind son: 25% - Color-blind daughter: 25%

Step-by-step solution

1. Identify the genotypes of the parents

The problem states that both the husband and the wife have normal vision, but both of their fathers are red-green color-blind. Since the color-blindness gene is X-linked recessive, we can determine their genotypes: - The husband (the male) has XY chromosomes, and since he is not color-blind, his genotype must be X^NY (N stands for normal, and his Y chromosome does not carry the colorblind gene). - The wife (the female) has XX chromosomes. As both her father and her paternal grandfather were colorblind, she must have inherited an X^N chromosome from her mother, but since she is not colorblind, her genotype must be X^NX^R (R stands for color-blind).

2. Create a Punnett square

Now, we will create a Punnett square to determine the genotypes of their potential offspring. With one letter from each parent, the square will look like this: X^N (from father) Y (from father) X^N (from mother) X^NX^N X^NY X^R (from mother) X^NX^R X^RY

3. Calculate the probabilities

Using the Punnett square, we can now calculate the probability for each type of child: (a) For a normal son (X^NY): The probability is 1 out of 4 squares, so the probability is 1/4 or 25%. (b) For a normal daughter (X^NX^N): The probability is 1 out of 4 squares, so the probability is 1/4 or 25%. (c) For a color-blind son (X^RY): The probability is 1 out of 4 squares, so the probability is 1/4 or 25%. (d) For a color-blind daughter (X^NX^R): The probability is 1 out of 4 squares, so the probability is 1/4 or 25%. Final probabilities for their first child: - Normal son: 25% - Normal daughter: 25% - Color-blind son: 25% - Color-blind daughter: 25%

Key concepts

Punnett square

The Punnett square is a simple yet powerful tool in genetics. It helps visualize how alleles from each parent contribute to the genotype of their offspring. For this exercise, the Punnett square illustrates possible genetic combinations arising when a couple with specific genetic traits has children.

The mother has the genotype X^NX^R and the father has X^NY. The Punnett square arranges these alleles in a grid format to consider all combinations:

• X^N from the mother and X^N from the father for a normal daughter.
• X^R from the mother and Y from the father for a color-blind son.
• X^N from the mother and Y from the father for a normal son.
• X^R from the mother and X^N from the father for a color-blind daughter.

The square provides a visual representation of probabilities, highlighting how each child's traits depend on these genetic combinations.

genotype

A genotype refers to the genetic makeup of an individual, specifically the alleles present at a particular gene locus. In this scenario, the genotypes help predict the chance of the couple having a child with normal vision or color-blindness.

• The male spouse has an XY genotype with an X^N chromosome, since he's not color-blind. His Y chromosome doesn't contribute to color vision traits.
• The female spouse is genotype X^NX^R, possessing one normal vision allele and one color-blindness allele because she inherited the color-blindness allele from her father.

Understanding these genotypes is crucial for determining the possible allele combinations in their offspring and the associated health traits.

sex-linked traits

Sex-linked traits are those that are associated with genes found on sex chromosomes; in humans, these are the X and Y chromosomes. Many sex-linked traits are found on the X chromosome and are thus called X-linked traits, like red-green color blindness.

• In X-linked inheritance, males (XY) are more likely to express recessive traits as they have only one X chromosome, and a single recessive allele will result in the trait.
• Females (XX) require two copies of a recessive allele to express such a trait. Therefore, in this exercise, the female spouse, carrying one normal and one color-blind allele, does not exhibit color-blindness because of the presence of the normal allele.

Understanding sex-linked traits helps in predicting how certain conditions can be inherited across generations, especially in cases of X-linked recessive conditions.

genetic probability

Genetic probability is the likelihood of inheriting particular genetic traits or alleles. When parents have alleles for specific traits, we can use tools like the Punnett square to calculate these probabilities.

For instance, each child has a 25% chance of being a normal son, normal daughter, color-blind son, or color-blind daughter based on the Punnett square outcomes in this exercise.

Genetic probability is grounded in Mendelian genetics, utilizing the laws of inheritance which include:

• Law of Segregation: Each parent contributes one allele for each trait.
• Law of Independent Assortment: Traits are passed on independently of one another.

By calculating probabilities with these laws, one can predict the genetic outcomes for offspring, which can be invaluable in understanding and preparing for inheritable conditions.