Introduction to Probability: 4600 Solved Problems and Practice Exercises Involving Dice, Marbles, Coins, and More!

Book Description

Probability is where Common Sense meets MathematicsProbability Theory is at the heart of almost every rational decision we make in our lives.It lies at the heart of every game of chance, and huge sums are won and lost based on split-second mental calculations of the probability that a choice made is likely to win.It lies at the heart of decisions we make about purchases and investments: all cost-benefit analyses rely on probabilistic projections of the probable benefit in the most likely future case.Probability Theory can be unbelievably complex to master at the highest level.However, the basics of this important field of mathematics and economics are very simple.This book is dedicated to the basics of probability theory.The target audience for this book is quite large. Anyone who wants a first course in probability or a refresher course in the subject can go through the theory, the solved problems, and the practice exercises in this book with much profit.The book starts with a detailed examination of one of the most common examples in any introductory textbook on probability: dice. As I take the reader through every case when 1 die, 2 dice, and 3 dice are rolled, I make sure that understanding of the subject is motivated through the many case studies that I have chosen; dozens of different solved examples have been presented to the reader so that you will be armed with the tools to tackle any real life problem.I then take you through two more classic introductory probability examples: coins and marbles. These illustrate many points that a more advanced student of probability will find useful, and lay a strong foundation for conditional probability.Finally, you will be given a large number of practice problems, of slowly increasing levels of difficulty. These are great for you to test your understanding of the topic, and slowly level up as you tackle questions that require a deeper understanding, or greater numerical skills. By the end of the book, you will be able to produce an error free answer to any elementary probability problem. In case you are unable to solve any problem, detailed solutions are provided at the end of the book.The long term advantages of a thorough reading of this book are many. A strong foundation in basic probability will increase your common sense skills, and help you make choices based on concrete estimates based on data given, rather than making random guesses. It is especially important for students of business and any scientific field to make these decisions, and is equally important for professionals in any field to understand probability.All the best!

中文：

书名：概率导论：4600道已解决的问题和练习，涉及骰子、弹珠、硬币等！

概率是常识与数学的交汇点概率理论是我们生活中几乎每一个理性决策的核心。它是每一场机会游戏的核心，基于对一个选择可能获胜的概率的瞬间心理计算，会有巨额的输赢。它是我们做出购买和投资决策的核心：所有的成本效益分析都依赖于对最有可能的未来情况下的可能收益的概率预测。在最高水平上掌握概率理论可能会令人难以置信地复杂。然而，数学和经济学这一重要领域的基础知识非常简单。这本书致力于概率论的基础知识。这本书的目标受众相当大。任何想要上概率学的第一堂课或复习课程的人，都可以通过这本书中的理论、解决的问题和实践练习来获得很大的收益。这本书的开头是对任何概率入门教科书中最常见的例子之一的详细检查：骰子。当我带读者看每一个掷骰子、2个骰子和3个骰子的案例时，我确保通过我选择的许多案例研究来激发对这个主题的理解；数十个不同的已解决的例子已经呈现给读者，以便你将拥有解决现实生活中任何问题的工具。然后带你通过两个更经典的入门概率例子：硬币和弹珠。这些说明了概率学较高级的学生会发现有用的许多点，并为条件概率学奠定了坚实的基础。最后，你将被给予大量的实践问题，难度逐渐增加。这些对测试你对主题的理解是很好的，当你解决需要更深层次的理解或更强的数字技能的问题时，慢慢地提升水平。到本书结束时，你将能够给出任何基本概率问题的无错误答案。如果你无法解决任何问题，在书的末尾提供了详细的解决方案。彻底阅读这本书的长期好处是很多的。扎实的基本概率基础将提高你的常识技能，并帮助你基于给定数据的具体估计做出选择，而不是做出随机猜测。对于商业和任何科学领域的学生来说，做出这些决定尤其重要，对于任何领域的专业人士来说，理解概率也同样重要。祝你一切顺利！