Probability theory

Probability theory is the part of mathematics that studies random situations.^{[1][2][3][4][5][6]} Probability theory usually studies random events, random variables, stochastic processes, and non-deterministic events (events that do not follow a simple pattern).

Tossing a coin, winning the lottery, or rolling a die are random events. However, random events have certain patterns, which can be studied and predicted, using probability theory.^{[2][3][4][5][6]}

Scientists can use probability theory to obtain information about things that would be too complex to deal with,^{[2][3][4][5][6]} like statistical mechanics.^[7][8][9] Also, scientists discovered (in the 20th century) that atoms, and everything that we know, obeys something called quantum mechanics,^[10][11][12] which uses lots of probability theory.

1. ↑ Probability theory, Encyclopaedia Britannica
2. ↑ ^{2.0 2.1 2.2} Chow, Y. S., & Teicher, H. (2003). Probability theory: independence, interchangeability, martingales. Springer Science & Business Media.
3. ↑ ^{3.0 3.1 3.2} Feller, W. (2008). An introduction to probability theory and its applications (Vol. 2). John Wiley & Sons.
4. ↑ ^{4.0 4.1 4.2} Durrett, R. (2019). Probability: theory and examples (Vol. 49). Cambridge University Press.
5. ↑ ^{5.0 5.1 5.2} Jaynes, E. T. (2003). Probability theory: The logic of science. Cambridge University Press.
6. ↑ ^{6.0 6.1 6.2} Chung, K. L., & Zhong, K. (2001). A course in probability theory. Academic Press.
7. ↑ Tolman, R. C. (1979). The principles of statistical mechanics. Courier Corporation.
8. ↑ Ruelle, D. (1999). Statistical mechanics: Rigorous results. World Scientific.
9. ↑ Thompson, C. J. (2015). Mathematical statistical mechanics. Princeton University Press.
10. ↑ Flügge, S. (2012). Practical quantum mechanics. Springer Science & Business Media.
11. ↑ Griffiths, D. J., & Schroeter, D. F. (2018). Introduction to quantum mechanics. Cambridge University Press.
12. ↑ Baym, G. (2018). Lectures on quantum mechanics. CRC Press.