A remark on an old problem of induction (Q1206020)

Consider a finite population of \(N\) balls (\(N\) known), \(R\) of which are red (\(R\) unknown). A sample of \(n\) balls is drawn without replacement and \(T\) is the number of red balls in the sample. Suppose we observe \(T=n\): we want to test the hypothesis that all the \(N\) balls in the population are red. This is a very old problem and the only way to tackle it seems to be a Bayesian way. Bayesian hierarchical priors are used to propose a quite general method of solution which includes the already known proposals.