Distance between Random Points on the X and Y Axes

Probability Level 3

Point AA is chosen randomly on the yy-axis between y=0y=0 and y=1,y=1, while point BB is chosen randomly on the xx-axis between x=0x=0 and x=1x=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 pq\frac{p}{q}, where pp and qq are coprime positive integers. What is 3p+4q?3p+4q?

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