Two circles are to be constructed as follows. Circle $A$ has radius $0.5$, and its center is chosen uniformly and at random from the line segment joining $(0,0)$ and $(3,0)$. Circle $B$ has radius $1.5$, and its center is chosen uniformly and at random, and independently of the first choice, from the line segment joining $(0,\sqrt{2})$ to $(2,\sqrt{2})$. What is the probability that circles $A$ and $B$ intersect?