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<h2><span style="font-family:Times New Roman,Times,serif"><span style="font-size:14pt"><span style="color:#0070c0"><strong>History Related to Probability</strong></span></span></span></h2>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">It is frequently said that something is “probably the case” or “probably not the case.” The word “probable” comes from the Latin word “probabilistic” which means “commendable”. Well, the English “probable” and “provable” have the same etymology origin. By doing scientific research of probability, we get to know that it takes the everyday ideas of recommending and gives them explanations and standardised calculation, something that tapers their preoccupation while strengthening their strength to notify.</span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif"> The very first listed proof of the theory of probability was found hopefully in the year 1550 by Cardan. In 1550 Cardan invented a manuscript in which he clearly stated that probability is an event or incident which exactly means how likely it might happen. If by chance, this manuscript became lost, then we would remain in the dark about the existence of probability. However, the manuscript did not come in the notice until 1576 and later it was printed in 1663, and then the discovery came to worldwide.</span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">In the dilemma of gambling game, the Modern Theory of Probability began in a 1654 similarity between de Fermat and Pascal about the problem of points. Once a dispute occurred in a gambling game, and from then the chapter “Probability” was discovered in 1654 by two famous French mathematicians, Blaise Pascal and Pierre de Fermat. </span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">Antoine Gombaud and Chevalier de Méré, the two French noblemen who had a passion for gambling, showed their interest in gaming and gambling questions. They referred Pascal’s mystery of the popular dice game as a probability. The rule of the game is to throw the dice 24 times. It is better not to bet your money or house unless the last double six occurs. This strange gambling rule led is one of the striking features and so it became very popular worldwide.</span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">Whereas the Dutch scientist Christian Huygens, who is also a teacher of Leibniz, in 1657 disclosed his first book on probability, which he named “De Ratiociniis in Ludo Algae’, it was written about the problems associated with gambling. This subject “probability” introduced as one of the chapters in mathematics after his book came to the market. The names must be mentioned Jakob Bernoulli and Abraham de Moivre. </span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">In 1812 a mathematician named Pierre de Laplace stated about his mass of new ideas and mathematical procedures in his book named “Théorie Analytique des Probabilités”. Before the theory placed by Laplace, this was only concerned as one of the chapters in mathematics. Laplace later applied his own ideas of probabilistic to various scientific and practical difficulties. These chapters made us think about the probable things that occur everywhere.</span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">Probability has also gained popularity just like the other branches of mathematics during the 18 century. Day by day, everyone is using this their and get to explore the ideas. Mathematical statistics is one of the important mathematical applications. Other notable applications which are used in different fields are genetics, psychology, economics, and engineering. Many employees have participated in the theory since Laplace’s time; among them, the important names are Chebyshev, Markov, von Mises, and Kolmogorov.</span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">Now the main problem which occurs is regarding the exact definition. People got the idea as well as the importance of probability of. But it is also important to find the proper definition. The scientists took almost three centuries to frame the definition. Ultimately, the problem got its solution in the 20th century. In 1933 a Russian mathematician A. Kolmogorov outlined the proper definition. He discussed with his colleagues and came to a conclusion. Ultimately, people got the idea as well as the proper and exact definition of probability.</span></span></span></p>
<p><span style="font-family:Times New Roman,Times,serif"><span style="color:#000000"><span style="font-size:16px"><strong> </strong>The first major achievement in the expansion of probability theory was the culmination that one could realise or predict the actual outcome. The second major achievement is primarily communicated in the 18th century, was the idea that probability and statistics are two branches of science and they both deals with limitless entreaty and chances. It was the early work of the scientist’s named Pascal, Fermat, Grant, Bernoulli, DeMoivre, and Laplace. They set the theory of probability and later statistics also. It is one of the important discovery of science today. Since then, probability theory became part and parcel of our life. We use daily the word ‘probability’. </span></span></span></p>
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<h2><span style="font-family:Times New Roman,Times,serif"><span style="font-size:14pt"><span style="color:#0070c0"><strong>The Spread of Statistical Mathematics</strong></span></span></span></h2>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">The statistical mathematics spread when the evolution of sciences began. Rather I would say that at least a century before there were many professional statisticians a century before. After the discovery of probability, life became easier for many people. Other than that, the calculations of some situations have also become easy in the 19th and 20th centuries. Between these centuries, the famous German mathematician Carl Friedrich Gauss published his new derivation to the world and made the new discovery and showed us the least-squares which incorporate a mathematical function and people came to know as the astronomer’s curve of error, and later his identity became Gaussian and normal distribution also.</span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">Many astronomers predictions came to conclusion about the several parameters which had been later discussed in the 18th century. The whole problem was explained to the worldwide and no one faced any problems. Thus people were totally aware of the fact that probability could play a lot of roles. You can refer this to be one of the standard measures of length in the new metric system, established during the French Revolution and the measurement is 1/40,000,000 of the total circumference of the Earth. The French mathematician Adrien-Marie Legendre in the year 1805 decided to solve this problem by selecting the values which would minimise the sums of the squares of deviations of the particular observations from a point, line, or curve which are drawn through them. You can say where all the observations were measures in a single point, this method was comparable in taking the <a href="https://doubtnut.com/question-answer/arithmetic-mean-sum-of-all-observations-number-of-observations-1528156">mean of arithmetic</a>.</span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">After the publication of the theory, Gauss showed his interest in the branch of mathematics of least squares, and he also gave us an example in 1809 that this method proved to be the best possible solution of a parameter if the mistakes of the quantities were determined to follow the normal distribution. This scattering, whose significance in mathematical probability and statistics was definitive, was first formulated by the famous French mathematician Abraham de Moivre in the year the 1730s to be the limit for the <a href="https://doubtnut.com/question-answer/formula-of-mean-and-variance-of-binomial-distribution-proof-1340584">binomial distribution</a>. In other words, this means that a continuous function and the power of calculus could be transferred for a discrete function and new techniques of numerical methods. Laplace cleverly used the distribution of dices vastly as a part of his own strategy, and he applied the causes of probability in various cases. One of the severe most problem of this kind in the 18th century is to estimate the actual populations.</span></span></span></p>
<p><span style="color:#000000"><span style="font-size:16px"><span style="font-family:Times New Roman,Times,serif">Laplace played an important role in formulating the formula twice by applying the procedure of least squares which is mainly the difficulty in dealing with probabilities. In the 19th century, many new derivations came by scientists. It had an important role in the newly discovered subjects like Astronomy, Geodesy, and some related measurement disciplines, which include the psychological factor. After that in the era of 1900, it bestowed a mathematical basis for a broader space of statistics which came to be used by a vast expanse of areas.</span></span></span></p>
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