 Consider first the problem of direct inference. Given the proportion of white balls in the urn, what is the probability of various outcomes for a sample of observations of a given size? Suppose the proportion of white balls in the urn is \(\theta = 0.6\). The probability of drawing one white ball in a sample of one is then \(p(W; \theta = 0.6) = 0.6\). We can also compute the probability for other outcomes, such as drawing two white balls in a sample of two, using the rules of the probability calculus (see section 1 of Hájek 2011). Generally, the probability that \(n_w\) white balls are drawn in a sample of size N, is given by the binomial distribution: