A Short Note on Types of Probability

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The probability of any given event occurring is defined as the probability. The outcome of any given event may be certain or uncertain. Probability has a number of applications in the field of games, in business to create probability-based forecasts, and in this new area of artificial intelligence.

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Definition of Probability

The Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of any given event. The number of favorable outcomes can be expressed by “x” in an experiment and ‘n’ is expressed as the total number of outcomes.

Probability of any given event = Favorable Outcomes/Total Outcomes = x/n 

By dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be estimated using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring can range between 0 and 1. Furthermore, the number of favorable outcomes cannot be negative.

Terminology related to Probability 

The terminology in probability listed below can help you comprehend probability ideas better.

• Experiment: An experiment is a trial or operation that is carried out to generate a specific result.
• Sample space: A sample space is the collection of all the probable outcomes of an experiment.. For example, a sample space of Tossing the coin is head and tail.
• Favorable Outcome: A favorable outcome is an event that has delivered the anticipated result or predicted event. When we roll two dice, for example, the possible/favorable outcomes of having the sum of the two dice as 4 are (1,3), (2,2), and (3,2). (3,1).
• Random Experiment: A random experiment is an experiment with a well-defined set of outcomes. When we toss a coin, for example, we know whether we will get heads or tails, but we don’t know which one will appear.
• A random experiment’s total number of results is referred to as an event.
• Equally Likely Events: Equally likely events are those that have the same possibility or probability of occurring. The outcome of one given event has no bearing to the outcome of the other. When we toss a coin, for example, we have an equal probability of getting a head or a tail.
• Exhaustive Events: The exhaustive event can be defined when the set of all possible outcomes of an experiment equals the sample space.

Types of Probability

Depending on the nature of the outcome or the method used to calculate the chance of an event occurring, several views or types of probabilities may exist. There are four major different types of probabilities:

• Classical Probability
• Axiomatic Probability
• Subjective Probability 
• Empirical Probability

Let us understand each type of probability one by one,

Classical Probability

Classical probability which is also known as the theoretical probability which further states that if there are B equally likely outcomes in an experiment and event X has exactly A of them, 

Then the probability of X is A/B, or P(X) = A/B.

It entails tossing a coin or rolling dice. It’s computed by making a list of all the possible outcomes of the activity and keeping track of what actually happens. When throwing a coin, for example, the possible outcomes are heads or tails. If you toss the coin ten times, you must keep track of which outcome occurred each time.

Axiomatic Probability

A series of rules or axioms by Kolmogorov are applied to all kinds of axiomatic probability. The probability of each event occurring or not occurring can be calculated using these axioms, which are written as,

• The smallest and greatest probabilities are 0 and one, respectively.
• The chance of a specific happening is equal to one.
• Only one of two mutually exclusive events can occur at the same time, according to the union of events.

Subjective Probability 

Subjective probability takes into account a person’s personal belief on the probability of an event occurring. For example, a fan’s opinion on the probability of a specific side winning a football match is based on their personal beliefs and feelings rather than a rigorous quantitative calculation.

Empirical Probability

Through thinking experiments, the empirical probability or experimental perspective evaluates probability. If a weighted die is rolled and we don’t know which side has the weight, we can gain an idea of the probability of each outcome by rolling the die a certain number of times and counting the proportion of times the die produces that outcome, and therefore find the probability of that outcome.

Conclusion:

• Probability is a metric for determining the probability of an event occurring.
• Probability is constantly between 0 and 1 and is expressed as a fraction.
• Probability is of 4 major types and they are, Classical Probability, Empirical Probability, Subjective Probability, Axiomatic Probability.
• The probability of an occurrence is the chance that it will happen. Any event’s probability is a number between (and including) “0” and “1.”