The expected area of the intersection between two shapes

Hi Everyone,

Assume a unit space (the extent on each dimension is 1). Assume that we have two shapes in the space A and B. The area of A is 1/x and the area of B is 1/y (both x an d y are greater than or equal to 1). The shapes are randomly placed in the space. What is the expected area of intersection between A and B (i.e., the area of $A\cap B$ ).

Is the following a right way to try solving this problem?

The probability that a randomly placed point p lies in A is 1/x. The probability that p lies in B is 1/y. The probability that p lies in both A and B is 1/x*1/y.

Please advise. Thank you

Best Regards,
mac