Probability of getting white ball If there are x black balls, y white balls and z red balls in a bag , r balls are drawn without replacement and now after this one more ball is drawn . What is the probability of this ball being white ??
Given : r <(x+y)
How to solve this? What approach do you recommend for these kind of questions ?

Imagine $r=1$.  The probability of drawing a white after drawing a single ball is
$$P(W|B) P(B) + P(W|W) P(W) + P(W|R) P(R)$$
which is
$$\frac{y}{x+y+z-1} \frac{x}{x+y+z} + \frac{y-1}{x+y+z-1} \frac{y}{x+y+z} + \frac{y}{x+y+z-1} \frac{z}{x+y+z}$$
which simplifies to $y/(x+y+z)$.  This experiment may be applied recursively, say $r$ times, so that the probability sought remains at  $y/(x+y+z)$ until there is a possibility of no more of a certain color of ball, i.e. $r \le \min\{x,y,x\}$.
