Final answer:
William's possible blood type is B with a genotype of BO, since he and Irene (blood type A), who carries the recessive O allele, have a child with blood type O.
Step-by-step explanation:
The question asks about the possible blood type of William given that he has parents with blood type B and his child with Irene, who has blood type A, is of type O. The blood type in humans is a classical example of inheritance of multiple alleles, which include IA (type A), IB (type B), and i (type O), with A and B showing codominance and both being dominant over O. Since William's parents both have type B blood, they could have the genotypes BB or BO. Therefore, William must have inherited one B allele from each of his parents. Given that Irene and William's child has type O blood, which is the ii genotype, William must be a carrier of the O allele to pass it to his offspring. This means William's genotype must be BO. Hence, William's blood type could be B.