69. Hypergeometric Probability Distribution. If samples are drawn from a relatively small finite population, and the sample size is larger than 1% of the population, so that the 1% Guideline (page 282) does not apply, we should not use the binomial distribution because the samples are not independent. Instead, if we are sampling without replacement, and there are two mutually exclusive categories, then you should use the hypergeometric probability distribution. Suppose that objects belong to the first category (“successes”), and objects belong to the second category (“failures”). Then the probability of getting successes and failures is given by the hypergeometric probability distribution formula:

where , is the population size, and is the sample size. You are dealt 5 cards at random from a deck of 52 cards.