You agreed to meet a friend of yours at Espresso Royale some time between noon and 1pm. Unfortunately, your cell phone died and you have no way of getting in touch with your friend. Both you and your friend have a busy schedule, so you will arrive at a random moment in time distributed uniformly between 12pm and 12:45pm, wait for 15 minutes and then leave if you don't see your friend. Your friend will do the same (assume your arrival times are independent). Find the probability that you and your friend will meet.
HINT: Draw a square picture, with the horizontal axis being time for you and the vertical axis being time for your friend. Shade in the part of the square where the two friends will meet (it will be a rectangular strip slanted at a 45 degree angle through the square, so there will some triangles at the two corners). Then find the area of the shaded part and divide by the area of the square.