Question

In humans, the \(A B O\) blood type is under the control of autosomal multiple alleles. Color blindness is a recessive X-linked trait. If two parents who are both type \(A\) and have normal vision produce a son who is color-blind and is type \(\mathrm{O},\) what is the probability that their next child will be a female who has normal vision and is type \(\mathrm{O} ?\)

Short answer

Answer: The probability is 1 in 8, or 12.5%.

Step-by-step solution

Determine the Parents' Genotypes

Since both parents have type A blood, they could have genotypes AA, AO. We know their son has type O blood, so they both must carry the O allele; thus, their genotypes are AO. Both parents have normal vision, so the mother's genotype is X^N X^N or X^N X^n and the father's genotype is X^NY.

Set up Punnett Square for Blood Type

Cross the parents' genotypes for blood type (AO x AO) in a Punnett square to find the possible blood types of their offspring. ``` A | O -------- A |AA | AO O |OA | OO ``` In this Punnett square, the probability that a child will have type O blood is 1 in 4 (OO).

Set up Punnett Square for Vision

Cross the parents' genotypes for vision (mother: X^N X^n, father: X^NY) in a Punnett square to find the possible genotypes of their offspring related to vision. ``` X^N | X^n --------- X^N |X^N X^N| X^N X^n Y | X^NY | X^nY ``` In this Punnett square, the probability that a child will be female with normal vision is 1 in 2 (X^N X^N).

Calculate the Probability of the Desired Combination

To find the probability that their next child will be a female with normal vision and type O blood, multiply the probabilities found in Steps 2 and 3: (1/4) x (1/2) = 1/8. The probability that their next child will be a female with normal vision and type O blood is 1 in 8, or 12.5%.

Key concepts

Understanding the Punnett Square

The Punnett square is a visual tool in genetics used to predict the possible genotypes of offspring based on the genotypes of their parents. It is named after Reginald Punnett, who devised the approach to demonstrate how alleles can segregate and recombine during sexual reproduction. The square is drawn as a grid, with one parent's alleles listed along the top and the other parent's along the side. Each square within the grid represents a possible genotype for an offspring.

For example, with blood types, the alleles can be A, B, or O. If two parents both have type A blood, but their genotypes are AO (since they can pass on an O), the Punnett square will show the four possible combinations for their children: AA, AO, OA, and OO. This grid effectively illustrates why there is a 1 in 4 chance of any child they have possessing type O blood. The simplicity and visual nature of the Punnett square make it invaluable in understanding genetics basics.

Autosomal Multiple Alleles

Unlike most traits, which are determined by a simple pair of alleles, some traits have more than two alleles governing them. This is known as multiple allele inheritance and is where genes on autosomal chromosomes (non-sex chromosomes) exhibit more than two forms. The human ABO blood group system is an excellent example of this concept, with three alleles involved: A, B, and O.

However, each person still inherits only two alleles (one from each parent), and the O allele is recessive to both A and B. Therefore, a child's blood type depends on the combination of alleles received from their parents. Because of multiple alleles, genetic outcomes can be more varied and complex. The step-by-step solution of the exercise utilizes this principle to deduce the parents' genotypes as AO, given that they have a type O offspring, indicating they both carry the recessive O allele.

X-linked Recessive Traits

Some genetic traits are linked to the X chromosome and exhibit a pattern of inheritance different from traits carried on autosomal chromosomes. X-linked traits are often recessive, meaning that the trait will only be expressed in females if they inherit two copies of the recessive allele (one from each parent). In males, who have only one X chromosome, the presence of a single recessive allele is sufficient for the trait to appear since there is no second allele to potentially mask its effects.

Color blindness is an example of an X-linked recessive trait. The exercise solution illustrates how to determine the probability of having a daughter with normal vision, which requires she inherit at least one X chromosome with the normal vision allele (denoted as X^N). The Punnett square shows that there's a 50% chance of a female offspring receiving two X^N alleles, given the potential for an X^n carrier mother. These concepts, paired with an understanding of Punnett squares, help dissect the genetic outcomes in such scenarios.