Question 21
Two circles of radius $1$ are to be constructed as follows. The center of circle $A$ is chosen uniformly and at random from the line segment joining $(0, 0)$ to $(2, 0).$ The center of circle $B$ is chosen uniformly and at random, and independently of the first choice, from the line segment joining $(0, 1)$ to $(2, 1).$ What is the probability that circles $A$ and $B$ intersect?