A. Mr. Essy must have the genotype OO.
B. Mrs. Essy must have the genotype AO.
Mr. Essy must have the genotype OO because he has type "O" blood.
In the ABO blood group system, individuals with type "O" blood have two O alleles (OO) and do not have the A or B alleles.
Also, Mrs. Essy must have the genotype AO because she has type "A" blood and individuals with type "A" blood can have either two A alleles (AA) or one A allele and one O allele (AO).
So, as her children include both type "A" (Matthew) and type "O" (Mark), she must have inherited one A allele and one O allele from her parents resulting in the AO genotype.