Correct length-biased sampling from family-size survey

In a town, you visit a school and ask **100 kids**: “How many children are in your family?” You observe: - 50 kids say their family has 1 child - 20 kids say their family has 2 children - 30 kids say their family has 3 children Now you go to a **random house** in the town, knock on the door, and ask: “How many children live here?” Assume every family has at least one child, and (for this question) family sizes are only 1, 2, or 3. **Question:** What is your best estimate of the probability that a randomly chosen house has **exactly 1 child**? Clarify any assumptions you need about how the 100 kids were sampled (e.g., uniformly at random from all children in town).