Statistics

Probablity is a way of expressing knowledge or belief that an event will occur or has occurred. The concept has been given an exact mathematical meaning in probability theory, which is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems.

Various Attempts to define probablity:-

There are basically various types of probabilities, each with its limitations. None of these approaches to probability is wrong, but some are more useful or more general than others.

1. Classical Probablity :-applies to equally probable events, such as the outcomes of tossing a coin or throwing dice; such events were known as “equipossible”.
2. Logical theories of probability retain the classical interpretation’s idea that probabilities can be determined a priori by an examination of the space of possibilities.
3. Subjective probability: A probability derived from an individual’s personal judgment about whether a specific outcome is likely to occur. Subjective probabilities contain no formal calculations and only reflect the subject’s opinions and past experience. It can be further classified as relative frequency approach, which is based on with repeated trials and confidence aproach.
4. Mathematical Set: In mathematics, a probability of an event A is represented by a real number in the range from 0 to 1 and written as P(A), p(A) or Pr(A). An impossible event has a probability of 0, and a certain event has a probability of 1. However, the converses are not always true: probability 0 events are not always impossible, nor probability 1 events certain.