Ah I guess it is quite complicated with a tree diagram. Have you tried just writing them down? That's what I would do.
So for probability of red : 1st time = 7/15. 2nd time = 6/14. 3rd time = 5/13.
You could do it like that and just multiply/add whatever you need. Personally that's how I would do it because I struggle with tree diagrams when it comes to more than two things.