[Math] From an urn containing a white and b black balls, balls are successively drawn without replacement until only those of the same colour are left.

Question

From an urn containing a white and b black balls, balls are successively drawn without replacement until only those of the same colour are left. What is the probability that balls left are white?

This is what I have done.
(https://i.stack.imgur.com/CZH2x.jpg)

But the answer which is given is :
a/(a+b)

I can't possibly make out how it's happening.

Answer 1

You can consider the problem as drawing balls and there is only one ball left. That's because when there are more than 1 ball left but all are the same color, it doesn't hurt to keep drawing out balls.

Also, there is the same probability of leaving any ball last.

So the probability is $\frac a{a+b}$