Factorizing

gives me the following:

.

We know that the area of the half-circle divided by the area of the whole square multiplied by 100 gives us the percentage that the half-circles occupies in the square. Then, 100% minus the percentage found gives us the percentage of the rest of the square, which is the probability we're looking for. But I've tried to find a concrete percentage but I couldn't, I'm a bit rusty tonight and it's getting late :p Tell me if you get anything new...

Those are the calculations for what I've stated above:

x 100

x 100

x 100

% = The percentage that the half-square occupies

100% -

%= The probability we're looking for...

129%

100% - 129% = -29%