I haven't done these kind of probability problems in a long time and trying to relearn. Here is a question that i'm having trouble with.
Q: An urn contains n white and m black balls which are randomly removed one at a time. If n > m, then what is the probability that there are always more white than black balls in the urn (until, of course, the urn is empty)? Explain why this probability is equal to the probability that the set of withdrawn balls always contains more white than black balls?
The answer is: (n-m)/(n+m)
I am thinking that the probability P(more white than black) is equivalent to the probability of drawing "(n-m) or less" white balls than black balls in a certain number of trials. now I am stuck. how do I proceed? Any help is appreciated.