Answer:
If the mother's blood type is O, and the child's blood type is B, a man would be exonerated from paternity if he has blood type A or O.
Explanation:
In the above case, if a mother has blood type O and her child has blood type B, a man can be exonerated from paternity only if his blood type is A or O, and responsible if he is type B or AB.
The blood type is defined by the presence of surface antigens in the red blood cell, called A and B. The presence of each antigen is determined by a gene present on the parental chromosomes.
By making a hypothetical crossing between mother and man, one can observe why he can be exonerated.
Man with blood type O
♂ O|O
♀ O|O
Alleles O O
O O|O O|O
O O|O O|O
The only possibility, in this case, is to have children with type O blood. No chance of children B.
Male with blood type A
♂ A|O
♀ O|O
Alleles A O
O A|O O|O
O A|O O|O
In this case there is a 50% chance that the children will be blood type A and 50% chance that they will be O. No chance of children B.
In the case of a man A|A the result is 100% probability of children A|O, and no probability of children B.
So, a man with blood types A (any genotype) and O, can be exonerated from paternity, since it is impossible for him to have a child of blood type B, when the mother is of blood type O.
