Question

A point is randomly chosen on a map of North America. Describe the probability of the point being in each location:

North America:
New York City:
Europe:

Answer 1

First fix the interpretation: you pick a point uniformly at random from the area of a map that shows only North America (i.e. the sample space is the map image/region of North America).

- North America: probability = 1 (the whole sample space).

- New York City: it depends how you treat “New York City.”
- If you mean the geometric city as a 2‑D region on the map, the probability = (area of NYC on the map)/(area of the whole map). In real units this is tiny: NYC ≈ 783–790 km² vs. North America ≈ 24.7 million km², so about 783/24,700,000 ≈ 3.2×10⁻⁵ (≈0.0032%).
- If you mean a single point (e.g. the city centre, or the name label), that has zero area and the probability = 0.

- Europe: 0, because Europe is not part of a map whose domain is only North America (unless the map includes an inset or shows Europe as well; then probability would be proportional to whatever area of Europe is actually drawn).

(Also note that if you pick uniformly on the paper/image rather than using true Earth surface area, use the printed image areas — projection and margins matter.)