I read about this, $$ p(R|r=0,NI_{1}) = {N\choose n+1}{N-R\choose n} \; (6.44)$$ but the probability can not be greater than 1, this expression is an apparent error. $I_{1}$ means the state of knowledge about the urn is that 0 < R < N, while the general sum $S = \sum_{R=0}^N{{R\choose0}{N-R\choose n-r}}= {N+1\choose n+1} $ is given by $I_{0}$ which means we do not know the state of the knowledge about urn at all, so the $S'= S - {N\choose n}\delta(r,0) - {N\choose n}\delta(r,n)$, and the S' should be the denominator. Finally i get the result is $$ p(R|r=0,NI_1) = \frac{N-R\choose n}{N\choose n +1}$$
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$\begingroup$ This question is not readable without getting back to the book and should be made self-contained. $\endgroup$– Xi'anNov 4, 2017 at 14:01
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$\begingroup$ Yes, when I come across problem while reading the book, i will post a question here. I will make question more clear next time. $\endgroup$– hello_godNov 4, 2017 at 14:28
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You will find this error discussed (along with many others) at the website http://ksvanhorn.com/bayes/index.html. For more information on Jaynes's book, see http://www.etjaynesinfo.com
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1$\begingroup$ Thank you! It would be better if you would edit this post to cite the specific error that was made, rather than requiring interested readers to follow the links. $\endgroup$– whuber ♦Oct 31, 2017 at 21:25