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 \(\operatorname{son},(d)\) a color-blind daughter?

Short answer

Answer: The probabilities are as follows: (a) normal son: 1/4, (b) normal daughter: 1/4, (c) color-blind son: 1/4, and (d) color-blind daughter: 0.

Step-by-step solution

Understanding the given information

Since both husbands and wives have normal vision, it means they are both carriers of the colorblind gene (Xc) inherited from their fathers, who were colorblind. Their genotypes are XcX for the wife and XcY for the husband.

Creating the Punnett Square

We will create a Punnett square for the possible genotypes of their children. In the rows, we will place the wife's alleles (Xc and X) and in the columns, we will place the husband's alleles (Xc and Y): Xc Y -------------- Xc | XcXc | XcY -------------- X | XX | XY

Identifying the outcomes

We can now identify the possible outcomes for their children based on the Punnett square: - XcXc (color-blind daughter) - XX (normal daughter) - XcY (color-blind son) - XY (normal son)

Calculating the probabilities

To find the probability of each outcome, we will calculate the ratio of the desired outcome among the four possibilities. (a) The probability of having a normal son (XY) is 1/4 (b) The probability of having a normal daughter (XX) is 1/4 (c) The probability of having a color-blind son (XcY) is 1/4 (d) The probability of having a color-blind daughter (XcXc) is 0/4 or 0, as it's not possible for them to have a color-blind daughter since the mother has a normal X chromosome. In conclusion, the husband and wife have probabilities of having: (a) a normal son: 1/4 (b) a normal daughter: 1/4 (c) a color-blind son: 1/4 (d) a color-blind daughter: 0

Key concepts

Punnett square

The Punnett square is a simple yet powerful tool in genetics that helps predict the probable genetic outcomes of offspring. By organizing and visualizing the possible alleles from each parent, it allows us to determine the likelihood of various combinations.

To construct a Punnett square for X-linked inheritance problems, we consider the chromosomes passed down by each parent. A female has two X-chromosomes (XX), while a male has one X and one Y chromosome (XY). The Punnett square for the provided example looks at a couple where both have fathers with red-green color blindness, which is an X-linked recessive condition. This means that their gene carriers are noted as follows:

• The wife has alleles X_c and X, indicating she is a carrier, having inherited the X_c from her father.
• The husband has alleles X_c and Y, also indicating he is a carrier, with the X_c coming from his color-blind father.

By crossing these alleles using a Punnett square, we can visualize the potential offspring genotypes.

genetics problems

Genetics problems often involve determining the probability of inheriting certain traits. Using basic Mendelian genetics, we apply concepts such as dominant and recessive alleles, along with the crucial tool of Punnett squares, to solve these problems.

In solving the exercise, we approached each possibility separately. Let's break it down:

• Each parent has an X chromosome carrying either a normal vision allele or a color-blind allele. The father, with his Y chromosome, will affect only his sons’ genotype for X-linked traits.
• We identified all possible outcomes, considering both daughters (XX) and sons (XY), and then calculated the probability of each genotype.

By understanding chromosome inheritance patterns, one can logically deduce the chance of each phenotype appearing in their offspring. This is a crucial skill for tackling various genetics problems.

color blindness inheritance

Color blindness, particularly red-green color blindness, is the most common type of X-linked recessive trait. An X-linked recessive trait means that the gene causing the trait is located on the X chromosome. This location makes inheritance patterns distinct between males and females because of their differing sex chromosomes.

In the context of color blindness:

• A son inherits an X chromosome from his mother and a Y from his father, making each male child affected if the X chromosome carries the recessive allele.
• Daughters, on the other hand, receive one X chromosome from each parent. They need two copies of the recessive allele to express the trait but can be carriers if they only have one.

In this specific problem, both parents can pass the carrier allele (X_c). However, due to the presence of a normal X chromosome from the mother, the daughter cannot be color-blind, instead may become a carrier, whereas the son could be normal or color-blind depending on which X-chromosome is inherited.