Discrete probability distributions are used when the characteristic being investigated is represented by an integer (count) value. For example the score on a playing dice can only be 1, 2, 3, 4, 5 or 6.
A discrete distribution could be used to show the probability of getting a particular score on a single throw of the dice. If only one dice was involved the distribution would be uniform; there is an equal chance of any score. If two die were thrown the score could range from 2 to 12, with the highest probability being a score of 7.
Examples of discrete distributions include the Binomial Distribution, the Hypergeometric Distribution and the Poisson Distribution.