The possible blood groups of the child would be determined by the alleles inherited from the parents. The A and O blood groups are determined by the IA, i, and i alleles for the ABO gene, where IA is dominant to i and i is recessive, meaning that it will only be expressed if there are two copies.
If the father has blood group A, he can have either IAIA or IAi genotypes, and if the mother has blood group O, she has ii genotype. Therefore, the possible genotypes of the child could be IAi or ii, which equals blood groups A or O.
Option 1 and 2 can be ruled out because blood group B or AB require at least one allele IB, which neither parent carries. Blood group B requires IBIB or IBi and AB requires IAIB. Hence, the son cannot have these blood groups.
Option 4 may seem correct, but since the parents cannot pass on a B or AB blood type, this option is incorrect.
Considering all the factors, the correct answer is Option 3, which says that the child`s blood group may be O.