Drawing balls from an urn with or without replacement is a classical problem in probability. Several elementary statistics textbooks use it to introduce the binomial and hypergeometric distributions.
Consider drawing two balls with or without replacement from an urn containing blue and red balls. Let the random variable represent the number of red balls. Then the possible values of correspond to the events . This Demonstration calculates the probabilities of these three events and shows the probability tree diagram that represents the set of all possible outcomes of the experiment . The probability of each outcome is shown on its branch.