Centre or Edge
A point is chosen uniformly at random inside the unit square. What is the probability that it is closer to the centre of the square than to the nearest side of the square? Give an exact closed form, or a decimal rounded to 4 places.
Related problems & prerequisites
Worth solving first
- Nearest Wall of a Triangle 6.0/10
- The Midpoint Chord 6.0/10
- Rounding a Ratio 5.0/10
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.