Final answer:
The probability that at least one child is the king's sister in a family of n children is 1 minus the probability of all children being boys, which is calculated as 1 - (1/2)^n.
Step-by-step explanation:
To find the probability that at least one child is the king's sister from a family of n children, where n ≥ 3, we need to consider the complementary probability that all children are his brothers (no sisters).
Assuming that the probability of having a boy or a girl is equal (1/2), and that each child's gender is independent of the others, the probability that all n children are boys is (1/2)^n.
Therefore, the probability of having at least one girl (sister) is 1 minus the probability of having all boys, which is 1 - (1/2)^n.