Final answer:
The disorder described is most likely inherited via an X-linked dominant pattern, as it appears in females more frequently than males and cannot be passed from affected fathers to their sons.
Step-by-step explanation:
The most likely mode of inheritance for a hypothetical human trait described by the student, which shows females affected twice as frequently as males, affected fathers who have affected daughters but never affected sons, and half the children of affected mothers and normal fathers being affected, is X-linked dominant. This is because males are hemizygous for the X chromosome and will express any allele present on it. Females have two X chromosomes, so they can be heterozygous carriers without expressing the trait or they can express the trait if they have inherited the affected allele from one of their parents. Given that affected fathers may have affected daughters but never affected sons, it reinforces the X-linked dominant pattern since fathers cannot pass their X chromosome to their sons, only the Y chromosome.