www.ijcrt.org © 2020 IJCRT | Volume 8, Issue 8 August 2020 | ISSN: 2320-2882 IJCRT2008213 International Journal of Creative Research Thoughts (IJCRT) www.ijcrt.org 2011 CONTRIBUTIONS OF SOME EUROPEAN MATHEMATICIANS IN THE DEVELOPMENT OF PROBABILITY THEORY: A HISTORICAL SEARCH Akhil Goswami 1 , Gautam Choudhury 2 , and Hemanta Kumar Sarmah 1 1 Department of Mathematics, Gauhati University, Guwahati-14, Assam, India. 2 Mathematical Sciences Division, Institute of Advanced Studies in Science and Technology, Paschim Boragaon, Guwahati-35, Assam, India. ABSTRACT In the historical search of contributions of some European Mathematicians in the development of Probability Theory, we have given particular emphasis on the works of Abraham De Moivre (1667-1754.), Thomas Bayes (1701-1761), Leonhard Euler (1707-1783), Pierre S. Laplace (1749-1827), Johann Carl Friedrich Gauss (1777-1855) and Sime / on Denis Poisson (1781-1840). The aim of this article is to highlight the contributions made by the well-known European Mathematicians towards development of Probability Theory. Key Words: Probability Theory, Dirac delta function, Beta function, Gamma function. 1. Introduction: R. A. Fisher [1959], once mentioned ‘More attention to the History of Science is needed, as much by scientists as by historians, . . . and this should mean a deliberate attempt to understand the thoughts of the great masters of the past, to see in what circumstances or intellectual milieu their ideas were framed, where they took the wrong turning or stopped short on the right track. A sense of the continuity and progressive and cumulative character of an advancing science is the best prophylactic I can suggest against the manic-depressive alternations of the cult of vogue’. Concepts of Probability have been around for thousands of years, but the Probability Theory did not arise as a part of Mathematics until the mid-seventeenth century. During 15 th century, calculations of Probabilities became more noticeable. In1494, Fra Luca Paccioli (1447-1517) wrote the first printed work on Probability, ‘Summa de arithmetica, geometria, proportioni e proportionalita’. In 1550, Geronimo Cardano (1501-1576), inspired by the Summa wrote a book about games of chance entitled ‘Liber de Ludo Aleae’ which was published after 100 years of his death [1]. Cardano presented the result of his theory on dice and with respect to the roll of a die. He wrote: “...in six casts each point should turn up once; but since some will be repeated, it follows that others will not turn up .” The use of ‘should turn up’ [1] in the articulation of this principle suggests that it is based upon the symmetry of the die having six sides, each of which is as likely as the other to occur. It is an intuitive concept and is used to introduce elementary probability calculation, even today. Galileo Galilei (1564 -1642), published an article giving explanation of observations from a random process. Galileo wrote ‘Sopra Le Scopertedei Dadi’ in response to a request for an explanation about an observation concerning the playing of three dice where possible combinations of dice sides totalling 9, 10, 11, and 12 are the same. In Galileo’s word [1]: “…it is known that long observation has made dice-players consider 10 and 11 to be more advantageous than 9 and 12.” Galileo explained the phenomenon by enumerating the possible combinations of the three numbers composing the sum. He was able to show that 10 will show up in 27 ways out of all possible throws (which Galileo indicated as 216). Since 9 can be found in 25 ways and this explains why it is at a ‘disadvantage’ in comparison to 10 [1]. In the mid-seventeenth century, a simple question was directed to Blaise Pascal (1623-1662) by a nobleman Chevalier de Méré. It is believed that this question led to the birth of Probability Theory. Chevalier de Méré betted on a roll of a die that at least one 6 would appear during a total of four rolls. From past experience, he knew that he was more successful than not with this game of chance. Tired of his approach, he decided to change the game. He then changed the bet to that he would get a total of 12, or a double 6, on twenty-four rolls of two die. Later, he realized that his old approach to the game resulted in more money. So, he asked his friend Blaise Pascal why his new approach