Problem : There are "k" white and "m" black balls in the box. We draw the balls without replacement. What is the probability, that durning the n-th draw ball will be white.
I don't have idea how to start.
[Math] Black and white balls-probability
probability
Best Answer
You can start to calculate that at the n-th draw the ball is white , where $n=1,2,3$. Suppose you have 3 white (w) balls and $2$ black ($b$) balls. Let denote $P(X_n=w)$ the probability that at the n-th draw the ball is white. Then we have
$P(X_1=w)=\frac{3}{3+2}=\frac35$
For $P(X_2=w)$ there are two ways: a) $ww$ and b) $bw$. The probabilities are
a) $\frac35\cdot \frac{3-1}{5-1}=\frac{3\cdot 2}{5\cdot 4}=\frac{6}{20}$
b) $\frac25\cdot \frac{3}{5-1}=\frac{2\cdot 3}{5\cdot 4}=\frac{6}{20}$
Therefore $P(X_2=w)=\frac{6}{20}+\frac{6}{20}=\frac{3}{5}$
Equivalent calculations can be done for $n=3$
This could be a start to solve the problem.