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What is A priori probability?
A priori probability is a term that is used in distinguishing the ways in which values for probabilities can be obtained and in particular, an "a priori probability" is derived solely by deductive reasoning where deductive reasoning is the process of reasoning from one or more general argument or premises to reach a logically certain conclusion.
One way of deriving a priori probability is the Principle of indifference where the principle of indifference is a rule for assigning Epistemic probability when there are n > 1 mutually exclusive as well as collectively exhaustive possibilities.
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This Principle of indifference has the character of saying that, if there are N mutually exclusive as well as exhaustive events and if they are equally likely, then the probability of a given event taking place is 1/N and so similarly the probability of one of a given collection of K events is K/N. One disadvantage of defining probabilities in the above-described method is that it applies only to finite collections of events.
In Bayesian inference where Bayesian inference is a method of statistical inference in which the Bayes rule is used to update the probability estimate for a hypothesis as additional evidence is learned and Bayesian updating is an important technique throughout statistics as well as especially in mathematical statistics.
By using the Bayesian inference, A Priori Probability is known as Prior probability or objective priors where the prior probability is a broader concept. prior probability distribution which is known as the prior of an uncertain quantity p.
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For example, suppose ‘v’ is the proportion of voters who will vote for the politician named Smith in a future election can be called the probability distribution that would express one's uncertainty about ‘v’ before the "data" is taken into account.
Priori probabilities are most often used within the deduction method of calculating probability because one must use logic to determine what outcomes of an event are possible in order to determine the number of ways these outcomes can occur.
For example, consider how the change of price of the share such that its price can increase or decrease or can remain the same and so according to a priori probability, it is assumed that there is a 1-in-3, or 33%, chance of one of the outcomes occurring all else remaining equal.
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