Urn Problem - Basic Urn Model

Basic Urn Model

In this basic urn model in probability theory, the urn contains x white and y black balls, well-mixed together. One ball is drawn randomly from the urn and its color observed; it is then placed back in the urn (or not), and the selection process is repeated.

Possible questions that can be answered in this model are:

  • Can I infer the proportion of white and black balls from n observations? With what degree of confidence?
  • Knowing x and y, what is the probability of drawing a specific sequence (e.g. one white followed by one black)?
  • If I only observe n white balls, how sure can I be that there are no black balls? (A variation on the first question)

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