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.
I know that this question has already been asked, but it won't let me comment and I have a question about it. I drew a picture and found the area of when they meet as 2025. So the probability I got was 9/16. I then tried 1-9/16=7/16, but this too was wrong. This however was wrong and now I am stumped again.
Any help would be appreciated. Thanks!