Hi everybody.(adsbygoogle = window.adsbygoogle || []).push({});

I keep on reading Rohatgi's book "An introduction to Probability and Statistics" and I have worked out the following problem:

"An urn contains r red marbles and g green marbles. A marble is drawn at random and its color noted. Then the marble drawn, together with c > 0 marbles of the same color, are returned to the urn. Suppose that n such draws are made from the urn. Prove that the probability of selecting a red marble at any draw is r/(r+g)."

I have obtained the following expression for the required probability:

[tex]

P(n) = \frac{1}{\prod_{j=0}^{n-1}(r+g+jc)} \sum_{k=0}^{n-1}(\stackrel{n-1}{k}) \prod_{j=0}^{k}(r+jc) \prod_{j=0}^{n-k-2}(g+jc)

[/tex]

This expression gives the result r/(r+g) for values n=2,3.

I have been trying to prove it for all values of n>=2, by induction, but with no success.

Perhaps anyone of you could help me.

Thanks and Happy Halloween !!

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# Conditional probability. Unable to prove the general result.

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