what is theoretical probability?

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There are various types of probability. Experimental (empirical) probability involves performing a number of trials and recording the outcomes. Subjective probability involves pattern recognition and professional judgement.

Theoretical probability is a type of probability that does not require performing an experiment. The probabilities of various events can be calculated just from the knowledge of the system in question. The theoretical probability is the number of outcomes in the event space (the number of outcomes that have the required attribute) divided by the number of outcomes in the sample space (the total number of possible outcomes.)

Examples include the probability of getting a certain number of heads from n flips, the probability of selecting a red ball then a blue ball from an urn, the probability of being dealt a straight flush in draw poker, etc...

Compare to empirical probability where you would use methods like a Monte Carlo simulation to compare many different trials of an experiment.

We can use theoretical probability to check whether a coin or die is "fair" by comparing the theoretical probabilities to the recorded empirical probabilities.

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