Probability

Probability is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0. An event with a probability of 1 can be considered a certainty: for example, the probability of a coin toss resulting in either "heads" or "tails" is 1, because there are no other options, assuming the coin lands flat. An event with a probability of .5 can be considered to have equal odds of occurring or not occurring: for example, the probability of a coin toss resulting in "heads" is .5, because the toss is equally as likely to result in "tails." An event with a probability of 0 can be considered an impossibility: for example, the probability of a coin toss resulting in "neither heads nor tails" is 0, because it's impossible for a coin to land without landing on either "heads" or "tails".

History

The modern probability theory, used widely in the fields of statistics, mathematics, science, engineering, and philosophy, was born in the 17th century. The scientific study of probability is a modern development of mathematics. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions arose much later.

Interpretations

There are several competing interpretations of probability. The interpretations of probability are a fundamental problem in the philosophy of probability. They can be divided into two broad categories: physical interpretations, which give physical meaning to probability, and evidential interpretations, which consider probability as a measure of the strength of evidence.

Applications

Probability theory is applied in everyday life in risk assessment and modeling. The insurance industry and markets use actuarial science to determine pricing and make trading decisions. Governments apply probabilistic methods in environmental regulation, where it is called pathway analysis.

See also

• Statistics
• Mathematics
• Science
• Engineering
• Philosophy
• Actuarial science
• Pathway analysis

References

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  Probability distribution of dice rolls

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  Portrait of Gerolamo Cardano

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  Painting of Christiaan Huygens

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  Portrait of Carl Friedrich Gauss

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  Graph showing probability vs odds

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  Diagram of independent and non-independent probability events