The pedigree shows an X‑linked dominant mode of inheritance, so the correct option is (4) X‑linked dominant inheritance.

Understanding the pedigree

Only females are affected, an affected mother has both affected and unaffected children, and there is no male‑to‑male transmission, which rules out autosomal patterns and strongly indicates an X‑linked dominant trait. In X‑linked dominant inheritance, one mutant allele on the X chromosome is sufficient to express the trait in both males and females, and affected females can pass the trait to 50% of all their children regardless of sex.

Option (1) Y‑linked inheritance

Y‑linked traits appear only in males, because the Y chromosome is transmitted strictly from father to son. In the given pedigree, affected individuals are females, immediately excluding a Y‑linked pattern, so option (1) is incorrect.

Option (2) X‑linked recessive and autosomal recessive

X‑linked recessive disorders show many more affected males than females, and unaffected carrier mothers can have affected sons while daughters are usually carriers. Autosomal recessive traits often skip generations and can appear in siblings with unaffected parents; neither of these features matches the continuous appearance of affected females in this pedigree, so option (2) is not supported.

Option (3) Autosomal dominant inheritance

Autosomal dominant traits typically affect males and females equally and allow father‑to‑son transmission because the gene is on an autosome. The absence of affected males and the sex‑biased appearance of the trait in this pedigree contradict autosomal dominant inheritance, making option (3) incorrect.

Option (4) X‑linked dominant inheritance

In X‑linked dominant inheritance, affected females (usually heterozygous) transmit the trait to about half of their sons and half of their daughters, and there is no male‑to‑male transmission. The pedigree pattern, with affected females and no affected males, fits this expectation best, so option (4) is the most consistent explanation.