# Probability Introduction

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Probability implies the likelihood or chance of the occurrence of an event. When an event is certain to happen then probability of occurrence of that event is 1 and when event cannot happen then the probability of that event is equal to 0. In other words, Probability gives the information about how likely an event can occur.

Classical definition of probability: If we have sample “S”, then probability of occurrence of event “E” is defined as:

P(E) = number of events/Total number of elements in sample space

Properties of Probability: There are two defining properties of probability.

1. The probability of occurrence of an event(Ei) lies between 0 and 1 (i.e. 0 <= P(Ei) <= 1)
2. If in a sample space, the given set of events are  mutually exclusive and exhaustive then the probability of those events sum to 1 (i.e. ∑P(Ei)  = 1)

Types of Probability:

Empirical Probability: An empirical probability is established by analyzing past data. In the Empirical probability also known as experimental probability we analyze the historical data to ascertain the probability of occurrence an event in future.

Experimental Probability = Number of times event occurred / Total number of times experiment performed

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 the 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.

Subjective Probability: A subjective probability is the least formal method of developing probabilities and involves the use of personal judgment.

In this series, we would cover properties of probability most commonly used in finance and credit risk.