Written by: He Jizhao (21-U5)
Designed by: Katelyn Joshy (21-U1)
At 11 pm, Andy was still struggling with his probability assignment. Scratching his head, he murmured to himself, “Huh? When should I multiply and when should I add the two results? It’s so confusing! I don’t get it!” Frustrated by such insurmountable math problems, Andy wondered why he was studying probability in the first place…
Probability is often deemed by many as a subject that cannot be applied in real life. This might not be the case, however. Allow me to show you the true prevalence of probability in our lives and hopefully, help you to appreciate its beauty too!
All incidents that seem to occur based on “luck” can be explained using a probability model. Think about it- small examples in daily life, such as the probability of getting a multiple choice question correct or the probability of two persons in a class having the same birthday, can be obtained using a probability model. Probability was actually invented to explain the supposedly “lucky” incidents we come across in our lives. However, the development of probability may not be what you have imagined for other branches of mathematics like number theory, whose development is initiated and continued by mathematicians.
Delving into a bit of history here- what if I told you that the development of probability was not initiated by mathematicians, but by gamblers?
A gambler’s dispute in 1654 led to the creation of probability by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. Chevalier de Méré, a French nobleman with a keen interest in gaming and gambling issues, called Pascal’s attention to an apparent contradiction concerning a popular dice game.
The game consisted of throwing a pair of dice 24 times; the problem was to decide whether or not to place a bet on the occurrence of at least a “double six” out of the 24 throws. A seemingly well-established gambling rule led de Méré to believe that betting on a double six in 24 throws would be profitable. Unfortunately, his calculations indicated the very opposite. This particular problem, along with other questions posed by Mere led to an exchange of letters between Pascal and Fermat. This was exactly how some of the most fundamental principles of the theory of probability came about!
The theory that Pascal and Fermat developed is known as the classical approach to computing probabilities. The theory states that- if we suppose a game has ‘n’ equally probable number outcomes, out of which ‘m’ outcomes correspond to winning, the probability of winning is m/n.
A Dutch scientist, Christian Huygens, learned of this correspondence and shortly (in 1657) published his first book on probability thereafter; titled ‘De Ratiociniis in Ludo Aleae’. Given the appeal of gambling at that time, this probability theory spread like wildfire and developed rapidly during the 18th century. Two mathematicians, namely Jakob Bernoulli and Abraham de Moivre, contributed significantly to the development of probability in this period. Moreover, throughout the 18th century, the application of probability moved from games of chance to scientific problems like the probability of being born female or male.
In 1812 Pierre de Laplace (1749-1827) introduced a host of new ideas and mathematical techniques in his book, Théorie Analytique des Probabilités. Laplace applied probabilistic ideas (yes, that is a word) to many scientific and practical problems. The theory of errors, actuarial mathematics, and statistical mechanics are examples of some of the important applications of probability theory developed in the 19th century.
However, an unprecedented period of stagnation and frustration soon followed. By 1850, many mathematicians found the classical method to be unrealistic for general use and attempted to redefine probability in terms of frequency methods. Unfortunately, these attempts never grew into fruition and the stagnation continued. In 1889, the famous Bertrand paradox was introduced by Joseph Bertrand to show that the principle of indifference may not produce definite, well-defined, results for probabilities if it is applied uncritically when the domain of possibilities is infinite.
Here we are, now in the 20th Century, where mathematicians seem to find new light amidst the stagnation. In 1933, A. Kolmogorov, a Russian mathematician, outlined an axiomatic approach that forms the basis for the modern theory. He built up a probability theory from fundamental axioms in a way comparable with Euclid’s treatment of geometry. Since then, his ideas have been refined and probability theory is now part of a more general discipline known as measure theory.
Bertrand paradox (probability) – Wikipedia. En.wikipedia.org. (2021). Retrieved 16 June 2021, from https://en.wikipedia.org/wiki/Bertrand_paradox_(probability).
Staff.ustc.edu.cn. (2021). Retrieved 16 June 2021, from http://staff.ustc.edu.cn/~zwp/teach/Prob-Stat/A%20short%20history%20of%20probability.pdf.
概率在生活中的应用. Xzbu.com. (2021). Retrieved 16 June 2021, from https://www.xzbu.com/1/view-5695902.htm.