Let X and Y be independent standard normal random variables.

a) Find P(X>0, Y>0).

Yes, it's easy. But get a piece of paper and draw the event on the plane anyway. Imagine the joint density surface over the plane, and try to imagine the relevant volume under the joint density surface as a quadrant-shaped slice of a bell-shaped cake. This will help you in the next two parts.

b) Find P(X>0, Y>X).

c) Find P(X>0, Y>3-sqrt(X))