Genetic question

Both Mrs. Smith and Mrs. Jones had babies the same day in the same hospital. Mrs. Smith took home a baby girl, whom she named Shirley. Mrs. Jones took home a baby girl, whom she named Jane. Mrs. Jones began to suspect, however, that her child and the Smith baby had been accidentally switched in the nursery. Blood tests were made: Mr. Smith was type A; Mrs. Smith type B' Mr. Jones type A; Mrs. Jones type A; Shirley type O; Jane type B. Had a mixup occured? Why did you answer the way you did?

http://www.paternityangel.com/Articles_zone/Blood/BloodType2.htm

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To determine if a mix-up occurred between Mrs. Smith and Mrs. Jones' babies, we need to analyze the blood types of the parents and the babies. Here are the blood types of each individual:

- Mr. Smith: Type A
- Mrs. Smith: Type B
- Mr. Jones: Type A
- Mrs. Jones: Type A
- Shirley (Mrs. Smith's baby): Type O
- Jane (Mrs. Jones' baby): Type B

Based on this information, we can make the following observations:

1. Both Mr. Smith and Mr. Jones have type A blood.
2. Mrs. Smith has type B blood.
3. Mrs. Jones has type A blood.

As per the rules of blood typing, the possible blood types that the babies could inherit from their parents are as follows:

- If both parents are type A (Mr. Jones), the baby can be type A or type O.
- If one parent is type A (Mr. Jones) and the other is type B (Mrs. Smith), the baby can be type A, type B, type AB, or type O.
- If both parents are type B (Mrs. Smith), the baby can be type B or type O.

Considering these possibilities, we observe that both Shirley and Jane have blood types that are consistent with their parents' blood types:

- Shirley has type O blood, which is possible if Mrs. Smith (type B) and Mr. Smith (type A) are her biological parents.
- Jane has type B blood, which is possible if Mrs. Jones (type A) and Mr. Jones (type A) are her biological parents.

Since the blood types of the babies are consistent with their parents' blood types, it can be concluded that no mix-up occurred in the hospital. Shirley belongs to Mrs. Smith, and Jane belongs to Mrs. Jones.

To determine whether a mix-up had occurred between the babies, we need to analyze the blood types of the parents and the babies. Blood type is determined by the presence or absence of certain markers, or antigens, on the surface of red blood cells.

Let's break down the blood types of the individuals involved:

Mr. Smith: Blood type A (genotype could be AA or AO)
Mrs. Smith: Blood type B (genotype could be BB or BO)
Mr. Jones: Blood type A (genotype could be AA or AO)
Mrs. Jones: Blood type A (genotype could be AA or AO)
Baby Shirley: Blood type O (genotype must be OO)
Baby Jane: Blood type B (genotype could be BB or BO)

To understand the likelihood of the mix-up, we need to determine the possible blood types that can be inherited from each parent. The ABO blood group system follows specific rules of inheritance:

- Blood type A (genotype AA or AO) can pass on either A or O allele to their offspring.
- Blood type B (genotype BB or BO) can pass on either B or O allele to their offspring.
- Blood type O (genotype OO) can only pass on the O allele to their offspring.

Given the blood types of Mr. Smith, Mrs. Smith, and Baby Shirley, we can conclude that Shirley must have inherited an O allele from both of her parents (since both Mr. and Mrs. Smith have at least one O allele possibility). Therefore, Shirley's blood type is consistent with her parentage.

Moreover, the blood types of Mr. and Mrs. Jones and Baby Jane are all compatible with the possible inheritance based on their blood types. Mr. and Mrs. Jones can both pass on the A allele, so it is possible for Baby Jane to inherit a B allele from Mr. Jones and an A allele from Mrs. Jones, resulting in her blood type B.

Based on this information, it appears that there was no mix-up in the nursery. The blood types of Baby Shirley and Baby Jane are consistent with their respective parents' blood types.

It's important to note that while blood type can provide evidence of biological relationships, it is not a definitive proof and may not be 100% conclusive. In some cases, DNA testing may be required for a more accurate determination.