Using probabilistic arguments, prove the identity ((A>a)) : [ 1+frac{A-a}{A-1}+frac{(A-a)(A-a-1)}{(A-1)(A-2)}+ldots+frac{(A-a) ldots 2 cdot 1}{(A-1) ldots(a+1) a}=frac{A}{a} ]

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Using probabilistic arguments, prove the identity $(A>a)$ :

\[ 1+\frac{A-a}{A-1}+\frac{(A-a)(A-a-1)}{(A-1)(A-2)}+\ldots+\frac{(A-a) \ldots 2 \cdot 1}{(A-1) \ldots(a+1) a}=\frac{A}{a} \]

An urn has $A$ balls, or which $a$ are white. The balls are drawn at random without replacement. Find the probability that sooner or later a white ball will be encountered.

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Theory Of Probability

ISBN: 9781351408585

6th Edition

Authors: Boris V Gnedenko

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Question Posted: May 06, 2024 04:02 AM

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Using probabilistic arguments, prove the identity ((A>a)) : [ 1+frac{A-a}{A-1}+frac{(A-a)(A-a-1)}{(A-1)(A-2)}+ldots+frac{(A-a) ldots 2 cdot 1}{(A-1) ldots(a+1) a}=frac{A}{a} ]

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Theory Of Probability

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