Answer:
Yes, an exchange has occurred between the two children
Explanation:
This question is trying to settle the issue of child exchange between two families (Doe and Roe). According to the question, the children were born in the same hospital. Roe family is said to have given birth to a boy (Richard) even if Mrs. Roe is sure she had a female child while Doe family is said to have born a girl (Nancy).
The ABO blood group system is used to reveal this mix up. The ABO blood group system is controlled by a single gene with three alleles (IA, IB, I). Alleles iA and iB are codominant i.e. simultaneously expressed, but both dominant over allele I.
In the ABO system, the genotype determines the blood type:
Type A- iAiA or iAi
Type B- iBiB or iBi
Type AB- iAiB
Type O- ii
Based on this, the question states that Mr Roe is type O i.e. has a genotype ii while Mrs Roe is type AB i.e. has a genotype iAiB. If both genotypes are crossed (ii × iAiB), only type A (iAi) and type B (iAi) child can be born to the Roe family (see punnet square attached). This means that the boy (Richard) with type O blood group cannot be their child.
On the other hand, Mr and Mrs Doe are both type B blood group I.e. will have either iBiB or iBi genotype. If this two type B genotypes combine using a punnet square, a type A offspring, which their claimed daughter (Nancy) has, can never be produced. This shows that Nancy is not their child.
Mr Roe and Mrs Roe is likely the owner of the girl child (Nancy) with type A blood group while Mr Doe and Mrs Doe is likely the owner of the male child (Richard) with type O blood group. Hence, there was an exchange between the two children of both families at the hospital.
