The most common probability distributions are the normal, binomial, poisson, geometric and uniform distributions. Each can be used to model certain situations, and if approximations are allowed, more than one model is possible for any given situation. The normal distribution, can for example be used an as an approximation for any distribution under certain circumstance, because of the Central Limit Theorem.

The Normal Distribution – can be used to model symmetric bell shaped distributions. It cannot be theoretically used to model a distribution if there are restrictions on the values the distribution may take. For example, we cannot theoretically use it to model the lengths of snails, because there exists a lower limit of 0, but in practice the normal distribution is often used to model such situations. The normal distribution can be either a continuous, or using the continuity correction, discrete distribution.

The Binomial Distribution – can be used in any situation where the probability of success is fixed. The binomial distribution models the number of successes in n trial, where n is a fixed number. The binomial distribution is a discrete distribution since in n trials the number of successes is an integer.

The Poisson Distribution – can be used to model any distribution where events happen at a certain rate per unit time, or misprints happen on average at so many per page. Under some circumspances, where p is small – less than- and n is large – greater than 30 - the Poisson distribution can be used as an approximation to the binomial distribution. The Poisson distribution is an integer since the number of events in each time period is an integer.

The Geometric Distribution – used to model the number of attempts until the first success. The probability p has to be fixed so this distribution cannot be used to model learning games. The Geometric distribution is a discrete distribution, since the number of attempts must be an integer.

The Uniform Distribution. The probability of each outcome is the same. The set of values that may be taken has finite upper and lower limits, meaning that any observed value must be between two numbers. The uniform distribution can be either continuous or discrete.