Mathematics: Probability
Contents | Page | Part 1 | 2 | Part 2 | 5 | Part 3 | 6 | Part 4 | 8 | Part 5 | 10 | Further Exploration | 13 | Conclusion | 14 | Reflection | 15 |
Part 1
a) Introduction
The word Probability derives from probity, a measure of the authority of a witness in a legal case in Europe, and often correlated with the witness 's nobility. In a sense, this differs much from the modern meaning of probability, which, in contrast, is used as a measure of the weight of empirical evidence, and is arrived at from inductive reasoning and statistical inference.
A short history of Probability Theory............
The branch of mathematics known as probability theory was inspired by gambling problems. The earliest work was performed by Girolamo Cardano (1501-1576) an Italian mathematician, physician, and gambler. In his manual Liber de Ludo Aleae, Cardano discusses many of the basic concepts of probability complete with a systematic analysis of gambling problems. Unfortunately, Cardano 's work had little effect on the development
of probability because his manual, which did not appeared in print until 1663, received little attention.
In 1654, another gambler named Chevalier de Méré created a dice proposition which he believed would make money. He would bet even money that he could roll at least one 12 in 24 rolls of two dice. However, when the Chevalier began losing money, he asked his mathematician friend Blaise Pascal (1623-1662) to analyze the proposition. Pascal determined that this proposition will lose about 51% of the time. Inspired by this proposition, Pascal began studying more of these types of problems. He discussed them with another famous mathematician, Pierre de Fermat (1601-1665) and together they laid the foundation of probability theory.
Examples / Application & Importance of Probability Theory to real life situations................
Probability theory is concerned with determining the relationship between the number of times a
Part 1
a) Introduction
The word Probability derives from probity, a measure of the authority of a witness in a legal case in Europe, and often correlated with the witness 's nobility. In a sense, this differs much from the modern meaning of probability, which, in contrast, is used as a measure of the weight of empirical evidence, and is arrived at from inductive reasoning and statistical inference.
A short history of Probability Theory............
The branch of mathematics known as probability theory was inspired by gambling problems. The earliest work was performed by Girolamo Cardano (1501-1576) an Italian mathematician, physician, and gambler. In his manual Liber de Ludo Aleae, Cardano discusses many of the basic concepts of probability complete with a systematic analysis of gambling problems. Unfortunately, Cardano 's work had little effect on the development
of probability because his manual, which did not appeared in print until 1663, received little attention.
In 1654, another gambler named Chevalier de Méré created a dice proposition which he believed would make money. He would bet even money that he could roll at least one 12 in 24 rolls of two dice. However, when the Chevalier began losing money, he asked his mathematician friend Blaise Pascal (1623-1662) to analyze the proposition. Pascal determined that this proposition will lose about 51% of the time. Inspired by this proposition, Pascal began studying more of these types of problems. He discussed them with another famous mathematician, Pierre de Fermat (1601-1665) and together they laid the foundation of probability theory.
Examples / Application & Importance of Probability Theory to real life situations................
Probability theory is concerned with determining the relationship between the number of times a