Distance between Random Points on the X and Y Axes

Probability Level 3

Point $A$ is chosen randomly on the $y$ -axis between $y=0$ and $y=1,$ while point $B$ is chosen randomly on the $x$ -axis between $x=0$ and $x=1$ . Both events are independent of each other.

The expected value of the square of the distance between them can be expressed in the form $\frac{p}{q}$ , where $p$ and $q$ are coprime positive integers. What is $3p+4q?$