Final answer:
A child with type O blood can be born to parents who have blood types A and B if one of each of their genotypes include an O allele, such as AO and BO. Thus, the man with type B blood could potentially be the father of the child with type O blood.
Step-by-step explanation:
Based on the principles of ABO blood group inheritance, a child with type O blood, which has the genotype ii, can indeed be born to parents with blood type A and B. Specifically, if the mother has blood type A with the genotype AO, and the man in question has blood type B with the genotype BO, it is possible for them to produce a child with blood type O. Due to the child having type O blood, they inherit one recessive allele, i, from each parent.
Furthermore, when considering the inheritance patterns of ABO blood types, the presence of A and B alleles in the parents means both A and B alleles are dominant over the O allele. Therefore, for a child to have type O blood, each parent must contribute an O allele (i). The process of cross matching is not directly related to determining the potential for paternity but is a necessary step before blood transfusions to ensure compatibility.
Regarding the legitimacy of the paternity, this determination would require a precise paternity test, as ABO blood type alone cannot provide conclusive evidence. However, in this scenario, the blood types of the mother, child, and potential father do not exclude the possibility of paternity.