# Thread: independent of k balls

1. ## independent of k balls

from a bag conatining m white and n black balls a ball is drawn and then put back with k addtional ball of same color .then again a ball is drawn .what is the probabilty that ball drawn is white.
My work .the solution is and i have got the answer by considering two cases.
but my question is that why answer is independent of k ?.

2. ## Re: independent of k balls

Originally Posted by ayushdadhwal
from a bag conatining m white and n black balls a ball is drawn and then put back with k addtional ball of same color .then again a ball is drawn .what is the probabilty that ball drawn is white.
My work .the solution is and i have got the answer by considering two cases.
but my question is that why answer is independent of k ?.
\begin{align*}P(W_2)&=P(W_2\cap W_1)+P(W_2\cap B_1) \\&=P(W_2| W_1)P(W_1)+P(W_2| B_1)P(B_1) \\&=\frac{m+k}{m+n+k}\frac{m}{m+n}+\frac{m}{m+n+k} \frac{n}{m+n}\end{align*}

So what sense is it independent of k ?