# A Priori Probability - Explained

What is A Priori Probability?

# What is A Priori Probability?

A priori Probability refers to the logical estimation of an incidents probability. It can also be explained as a situation where one estimates a circumstance or current information about the position of something. This probability deals with independent event whereby the possibility of a given event happening is not in any way influenced by past events.

## How does A Priori Probability Work?

Priori probability calculation is often done through deductive reasoning. This is so because, in order to determine the number of the possible outcome of any occurence, one must apply logic. Also, this type of probability is based on prior information when making a conclusion.

## Examples of A Priori Probability

When tossing a coin, the possibility of it landing on a head or a tail in the second or subsequent toss is not in any way dependent on the first or previous result. Therefore, the chances of landing either side are equal hence the probability will definitely be 50%. The probability can also apply to a firms earnings where whether the firm will make a profit, a loss or break even at any given year, the probability of each of the events happening is equal. In this case, the probability will, therefore, be of each event occurring. It is important to note that in Priori probability, experts draw a conclusion about the outcome of an event before looking at any statistics. Meaning the Priori probability is used to estimate the occurrence of an event before the event actually happens.

## Priori Probability Types

There are two types of Priori probability. The difference between the two probability is explained using Bayesian inference. They are as follows:

• Priori-This refers to capturing of general knowledge about a given statistics before looking at it. This means conclusions about the data is made before it is analyzed.
• Posteriori- This represents knowledge that includes the results. This means, in this type of probability, the outcome of an event is included in the conclusive results. Meaning the data about an event is analyzed before a conclusion is drawn.

## Priori Probability Uses

• The Priori probability estimates are applied on a nonlinear equation root during an evaluation.

• The main advantage of using this method of calculation is that the procedure has no assumptions.

## Limitation of Using Priori Probability in Calculation

• The major limitation about prior probability is that it only applies to a specific set of events (it is finite). For this reason, it can only be calculated for those events that are naturally independent. This is because the probability of most events happening is through conditioning to a certain percentage. The experiment is, therefore, not applicable where the outcomes are likely not to be equal.
• The experiment may fail especially when the figure of the possible experiment results is infinite (immeasurable).
• Difficult to estimate probabilities to the desired accuracy. You will need large sample sizes in order to get accurate results.

## Key Takeaways

• The conclusion is made prior knowledge or before analyzing any data.
• It involves deductive reasoning (logic deduction).
• It has a basic assumption that the results of a random experiment are likely to be equal.