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Math Help - independent of k balls

  1. #1
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    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 ?.

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  2. #2
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    Re: independent of k balls

    Quote Originally Posted by ayushdadhwal View Post
    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 ?
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