Question

A type A woman is the daughter of a type \(\mathrm{O}\) father and a type \(\mathrm{A}\) mother. If she has children with a type \(\mathrm{AB}\) man, what are the following probabilities? A. A type \(\mathrm{AB}\) child B. A type \(O\) child C. The first three children with type \(A B\) D. A family composed of two children with type B blood and one child with type \(\mathrm{AB}\)

Short answer

The child has a 25% chance of being of type AB, there is a 0% chance of the child being of type O, the probability of the first three children being type AB is 1.56% and the probability of two children with B blood type and one with AB is also 1.56%.

Step-by-step solution

Determine Mother's Genotype

The mother is type A, but as the father is type O, she must be AO because the only allele she could have received from her type O father would be a O. Therefore, her genotype is AO.

Determine Father's Genotype

The father is type AB which means his genotype is AB. AB individuals express both A and B alleles.

Determine Child's Genotype Using Punnett Square

The Punnett square is used to determine all possible combinations of alleles that the child could inherit. The mother can pass either A or O and the father can pass either A or B.

Calculate Probabilities of Each Genotype

By using the Punnett square, we find the genotypes of children can be: AA (25%), AO (25%), AB (25%), or BO (25%). AA and AO will result in a type A phenotype. AB will result in a type AB phenotype. BO will result in a type B phenotype. An O phenotype is not possible as neither parent has two O alleles.

Answer the Specific Questions

A. The child has a 25% chance of being of type AB. B. There is 0% chance of the child being of type O. C. The probability of having the first three children with type AB would be \(0.25^3 = 0.015625\) or 1.56%. D. The chance of two children with B blood type and one with AB is \(0.25^3 = 0.015625\) or 1.56%, since each child is an independent event.

Key concepts

Blood Type Inheritance

Blood type inheritance involves understanding how alleles from parents are passed down to their offspring to determine blood type. Humans have four possible blood types: A, B, AB, and O, which result from combinations of three different alleles: A, B, and O.
- Type A can be AA or AO, meaning it can inherit an A allele from both parents or an A from one and an O from the other. - Type B can be BB or BO. Similarly, it can inherit a B allele from each parent or a B from one and an O from the other.
- Type AB results from having one A allele and one B allele, expressing both characteristics. This type is unique as it does not have a recessive component. - Type O is the simplest, always requiring two O alleles.
The exercise highlights the inheritance pattern from a type A mother (genotype AO) and a type AB father (genotype AB). Their children's potential blood types are influenced by these genetic combinations. Understanding which alleles are dominant or recessive helps in predicting the possible blood types of their children.

Genotype Probabilities

When calculating genotype probabilities, one must consider all possible genetic combinations resulting from parental alleles. This involves using a method called the Punnett Square to visualize these possibilities. With a mother of genotype AO and a father of genotype AB, the child's genotype can be:

• AA (25% probability)
• AO (25% probability)
• AB (25% probability)
• BO (25% probability)

These probabilities show the even split due to the equal chance of inheriting either of the two alleles from each parent. The exercise reveals key phenotypic outcomes from this genotype distribution: - AA and AO result in a type A phenotype. - AB gives a type AB phenotype. - BO results in a type B phenotype. Understanding these probabilities lays the foundation for answering questions about the likelihood of offspring possessing certain blood types.

Punnett Square Analysis

A Punnett Square is a graphical representation used to predict the genotypes of offspring from a particular genetic cross. It lays out all possible combinations of parental alleles by dividing them into two axes, one for each parent.
For this exercise, the mother (AO) and father (AB) form a square with parental alleles on the top and side. This helps visualize each potential genotype:

• Top Row: A, O from Mother
• Side Column: A, B from Father

From this matrix, you fill in the squares to show potential offspring genotypes: - Combine Mother’s A with Father’s A gives AA - Mother’s O with Father’s A gives AO - Mother’s A with Father’s B gives AB - Mother’s O with Father’s B gives BO
Each square has an equal chance, indicating a 25% probability for each genotype. This simple tool clarifies complex inheritance patterns and aids in calculating the probabilities of different blood type outcomes as seen in the provided questions.