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==Empirical vs Theoretical Probability==

==Empirical vs Theoretical Probability==

Theoretical (or estimated) probability is a calculated probability based upon a set of mathematical or scientific assumptions (including other probabilities). A simple example is theoretical probability that the chance of rolling two sixes on a pair of unbiased six-sided [[dice]] 1/36 (2.78%).

Theoretical (or estimated) probability is a calculated probability based upon a set of mathematical or scientific assumptions (including other probabilities). A simple example is the theoretical probability that the chance of rolling two sixes on a pair of unbiased six-sided [[dice]] is 1/36 (2.78%).

Empirical (or experimental) probability is calculated simply as the ratio of ''observed'' favourable outcomes to total samples taken. Thus if a pair of dice might be rolled a thousand times, with an observed occurrence of 26 pairs of sizes. This gives an empirical probability of 26/1000 or 2.60%. With a larger number of samples, the empirical probability would be expected to tend towards the theoretical value. If it does not, then either the experimental [[methodology]] or the theoretical calculation and its assumptions would be questioned. In the case of the dice, the most likely explanation would be that the dice in the experiment were not truly unbiased.<ref>http://regentsprep.org/Regents/math/ALGEBRA/APR5/theoProp.htm</ref>

Empirical (or experimental) probability is calculated simply as the ratio of ''observed'' favourable outcomes to total samples taken. Thus a pair of dice might be rolled a thousand times, with an observed occurrence of 26 pairs of sixes. This gives an empirical probability of 26/1000 or 2.60%. With a larger number of samples, the empirical probability would be expected to tend towards the theoretical value. If it does not, then either the experimental [[methodology]] or the theoretical calculation and its assumptions would be questioned. In the case of the dice, the most likely explanation would be that the dice in the experiment were not truly unbiased.<ref>http://regentsprep.org/Regents/math/ALGEBRA/APR5/theoProp.htm</ref>

In situations more complex than a pair of dice, the basis of theoretical probability calculations can become increasingly contentious, and the approach tends to be useful only in the case of limited or absent observational data. For example, when the outbreak of a new strain of [[influenza]] occurs, theoretical calculations of expected mortality rates are quickly produced based on extrapolation from other flu strains. These are soon superseded by actual mortality observations.<ref>http://seedmagazine.com/content/article/overestimating_avian_flu/</ref>  

In situations more complex than a pair of dice, the basis of theoretical probability calculations can become increasingly contentious, and the approach tends to be useful only in the case of limited or absent observational data. For example, when the outbreak of a new strain of [[influenza]] occurs, theoretical calculations of expected mortality rates are quickly produced based on extrapolation from other flu strains. These are soon superseded by actual mortality observations.<ref>http://seedmagazine.com/content/article/overestimating_avian_flu/</ref>