a point is randomly selected within the rectangle with vertices at (2,0), (2,2), (-4,2), and (4,0). What is the probability that the point's x-coordinate and y-coordinate are both positive?

Answer 1

since two-thirds of the rectangle lies on the left of the y-axis, that leaves 1/3 with positive x-coordinates.

So, p=1/3 that the x-coordinate is positive.
Since all the y-coordinates are positive, they don't affect the probability.

What about points on the axes? They are not positive, but the probability of picking any of them is zero. Seems odd, but there are so many more real numbers than integers that the chance of hitting 0 is 0. (see transfinite numbers for an explanation)