Final answer:
It cannot be definitively determined what the father's genotype is for the hitchhiker's thumb trait without additional information about the children's phenotypes. Thus, the option 4 is the correct answer.
Step-by-step explanation:
Based on the provided information about hitchhiker's thumb being a dominant trait and the genotypes of individuals labeled 1, 2, and 3 being aa, AA, and AA respectively, it's not possible to definitively determine the father's genotype without additional details about the inheritance pattern of hitchhiker's thumb in the children. If the hitchhiker's thumb follows a simple autosomal dominant inheritance, and assuming the children's genotypes infer from their phenotypes given the mother's genotype, then typically if none of the children have a hitchhiker's thumb, the father would be homozygous recessive (ww). However, if any child does have a hitchhiker's thumb and if the mother does not, the father must possess at least one dominant allele (W), making him either heterozygous (Ww) or homozygous dominant (WW). Without knowing the children's thumb status, the answer could be option 2 (Ww), option 1 (WW), or it cannot be determined from the given pedigree alone.