What Is A Priori Probability?

A priori probability is calculated by logically examining a circumstance or existing information regarding a situation. It usually deals with independent events where the likelihood of a given event occurring is in no way influenced by previous events. An example of this would be a coin toss. The largest drawback to this method of defining probabilities is that it can only be applied to a finite set of events as most events are subject to conditional probability to at least a small degree.

Key Takeaways

  • A priori probability stipulates that the outcome of the next event is not contingent on the outcome of the previous event.
  • A priori also removes independent users of experience. Since the results are random and noncontingent, nobody would be able to deduce the next outcome with any more chance of success than a layperson.
  • A good example of this is during a coin toss. No matter what was flipped prior, the odds are always 50% since there are two sides.

Understanding A Priori Probability

A priori probabilities are most often used within the deduction method of calculating probability. This is because you must use logic to determine the possible outcomes of an event in order to determine the number of ways these outcomes can occur.

Real World Example of A Priori Probability

A great example of a priori is flipping a coin. A fair coin has two different sides and each time you flip it has an equal chance of landing on either side, regardless of the previous toss' outcome. The a priori probability of landing on the "heads" side of the coin is 50%. Same with "tails." This could be applied to any game of random chance such as roullette, throwing dice, lottery numbers, etc.

Another example, and one where the phrase is more commonly attributed, is when the price of a share changes. Its price can increase, decrease or remain the same. Therefore, according to a priori probability, we can assume that there is a 1-in-3, or 33%, chance of one of the outcomes occurring (all else remaining equal).