I have a bag containing 3 red sweets and 4 yellow sweets.

I am feeling greedy and repeatedly choose a sweet at random, eating them as I go along, until there are only sweets of one colour left. What is the probability that when this happens when there are only yellow sweets remaining?

What is the probability of being left with just yellow sweets if I do the same thing but with a bag containing 2 red and 3 yellow sweets? Or 3 red and 5 yellow?

Can you generalise for r red sweets and y yellow sweets?