4696 words - 19 pages

Contents

No. | Title | Page |

1 | Introduction | 2 |

2 | Part 1 | 6 |

3 | Part 2 | 8 |

4 | Part 3 | 10 |

5 | Part 4 | 13 |

6 | Part 5 | 17 |

7 | Further Exploration | 21 |

8 | Reflection | 22 |

Introduction

Moral Values:

I have learned many moral values while completing this assignment. Better still, I got to know about the importance of applying these moral values into our daily lives. The first moral value is to cooperate with other people. The strategies and solutions of the questions in this project work were discussed among me and a group of friends. This makes things easier and saved a lot of time.

The management of time is also important to complete this ...view middle of the document...

2. to prepare myself for the demands of my future undertakings and in workplace.

3. to use technology especially the ICT appropriately and effectively.

4. to acquire effective mathematical communication through writing, and to use the language of mathematics to express mathematical ideas correctly and precisely.

5. to apply and adapt a variety of problem-solving strategies to solve routine and non-routine problems.

Introduction to probabilities:

Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such area of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and underlying mechanics of complex systems.

The scientific study of probability is a modern development. Gambling shows that there has been an interest in quantifying the ideas of probability for millennia, but exact mathematical descriptions of use in those problems only arose much later.

history of probabilities:

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Etymology

Probable and likely and their cognates in other modern languages derive from medieval learned Latin probabilis and verisimilis, deriving from Cicero and generally applied to an opinion to mean plausible or generally approved.

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Origins

Ancient and medieval law of evidence developed a grading of degrees of proof, probabilities, presumptions and half-proof to deal with the uncertainties of evidence in court. In Renaissance times, betting was discussed in terms of odds such as "ten to one" and maritime insurance premiums were estimated based on intuitive risks, but there was no theory on how to calculate such odds or premiums.

The mathematical methods of probability arose in the correspondence of Pierre de Fermat and Blaise Pascal (1654) on such questions as the fair division of the stake in an interrupted game of chance. Christiaan Huygens (1657) gave a comprehensive treatment of the subject.

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18th Century

Jacob Bernoulli's Ars Conjectandi (posthumous, 1713) and Abraham de Moivre's The Doctrine of Chances (1718) put probability on a sound mathematical footing, showing how to calculate a wide range of complex probabilities. Bernoulli proved a version of the fundamental law of large numbers, which states that in a large number of trials, the average of the outcomes is likely to be very close to the expected value - for example, in 1000 throws of a fair coin, it is likely that there are close to 500 heads (and the larger the number of throws, the closer to half-and-half the proportion is likely to be).

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Nineteenth century

The power of probabilistic methods in dealing with uncertainty was shown by Gauss's...

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