Abstract
If mathematics is the queen of sciences, then probability is the queen of applied mathematics. The concept of probability originated in the seventeenth century and can be traced to games of chance and gambling. Games of chance include actions like drawing a card, tossing a coin, selecting people at random and noting number of females, number of calls on a telephone, frequency of accidents, and position of a particle under diffusion. Today, probability theory is a well-established branch of mathematics that finds applications from weather predictions to share market investments. Mathematical models for random phenomena are studied using probability theory.
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Notes
- 1.
Andrey Nikolaevich Kolmogorov (1903–1987) was a twentieth-century Russian mathematician who made significant contributions to the mathematics of probability theory. It was Kolmogorov who axiomatized probability in his fundamental work, Foundations of the Theory of Probability (Berlin), in 1933.
- 2.
A smallest \(\sigma \)-field on \(\mathbb {R}\) containing all intervals of the form \((-\infty , a]\) with \(a \in \mathbb {R}\) is called the Borel \(\sigma \)-field on \(\mathbb {R}\) and is usually written as \(\mathscr {B}\).
- 3.
Thomas Bayes (1702–1761) was a British mathematician known for having formulated a special case of Bayes’ theorem. Bayes’ theorem (also known as Bayes’ rule or Bayes’ law) is a result in probability theory, which relates the conditional and marginal probability of events. Bayes’ theorem tells how to update or revise beliefs in light of new evidence: a posteriori.
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Selvamuthu, D., Das, D. (2024). Basic Concepts of Probability. In: Introduction to Probability, Statistical Methods, Design of Experiments and Statistical Quality Control. University Texts in the Mathematical Sciences. Springer, Singapore. https://doi.org/10.1007/978-981-99-9363-5_2
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DOI: https://doi.org/10.1007/978-981-99-9363-5_2
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