Question 1199989
.
A box contains N white and M black balls. Balls are randomly selected one at
a time, until a black one is obtained. If we assume that each selected ball is
replaced before the next one is drawn, What is the probability that
a) Exactly n draws are needed.
b) At least K draws are needed.
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            In this my post,  I will solve part  (a),   ONLY.



<pre>
Event in part (a) is the intersection of two indepedent events E and F.


    Event E is that first (n-1) draws are white balls.

    Event F is that the n-th draw is a black ball.


Therefore, the probability of event in part (a) is

    P(event in part (a) ) = {{{(N/(N+M))^(n-1)*(M/(N+M))}}}.    <U>ANSWER</U>
</pre>

Solved.