What is the probability that two uniform random points (to be precise: i.i.d. with respect to Lebesgue measure) in the square are such that center of the square lies in the circle formed by taking the points as diameter.
Edit: Problem wording made more mathematical.
Correct solutions by Barun Kumar Kejriwal, Akhil Kumar, Aastha Airan, Arpit Goyal and Yashoteja in comments! Thanks a ton.