## probability of a game of drawing balls

I am new to probability , I do one question and stuck for days. Would you all can give me a hint on it?

There are () balls in a bin. are black, and is red. players each draw a ball from the bin randomly in a round-robin fashion, until the red ball is drawn.

a) What is the probability that the th player draw the red ball, for ?

b) Suppose there are players, red balls and black balls in the bin, what is the probability that first player draw the red ball first?

I just think about the result of two players game,

am I doing in the right way or not, if yes, how should I compute this sequence?

c) Suppose the balls are drawn with replacement instead, what are the answers to a) and b)?

c)b)

+

Am I doing in the correct way?