Final answer:
Bill's genotype is Pp; he inherited the dominant allele for precocious puberty (P) from his heterozygous mother and the normal puberty allele (p) from his father.
Step-by-step explanation:
Bill's genotype for precocious puberty is Pp. Given that the condition is autosomal dominant and sex-limited, expressed only in males, we know that Bill received the dominant allele, P, from one of his parents and a normal puberty allele, p, from the other. Since Bill's mother underwent normal puberty, she is either Pp or pp. However, the presence of the same condition in two maternal uncles suggests that she carries the allele for precocious puberty and is likely heterozygous Pp. Thus, Bill's mother, heterozygous for the trait, passed the P allele to Bill, while his father, with normal puberty, is most likely pp, providing the p allele. As such, Bill has one copy of the P allele and one copy of the p allele, explaining his precocious puberty phenotype while his siblings, Jack and Beth, who presumably inherited p alleles from both parents, underwent normal puberty.