Probability with Permutations: An Introduction To Probability And Combinations

By Steven Taylor

Probability with Permutations

Understanding probability as unique and stimulating theory which goes beyond conventional mathematics, will give you better perspective of the world around you. The first part of the book explains the fundamentals of probability in clear and easy to understand way even if you are not familiar with mathematics at all and you are just starting your journey towards this particular field of science. In the following sections of the book, the subject is explained in wider context along with importance ofpermutations and combinations in probability and their applications to a variety of scientific problems as well as the importance of probability in real life situations.

By Downloading This Book Now You Will Discover:

• History of Probability
• Explanation of Combinations
• Probability Using Permutations and Combinations
• Urn Problems
• Probability and Lottery
• Probability and Gambling
• Applications of Probability
• And much much more!

Download this book now and learn more about Probability with Permutations!

• Language: English
• Publisher: Steven Taylor
• Release date: Dec 20, 2017
• ISBN: 9781386513346

Steven Taylor

Dr. Steven Taylor is a Professor and Clinical Psychologist in the Department of Psychiatry at the University of British Columbia. For 10 years he was Associate Editor of Behavior Research and Therapy, and now is Associate Editor of the Journal of Cognitive Psychotherapy. He has published over 100 journal articles, over 35 book chapters, and 8 books on anxiety disorders and related topics. His most recent books are on the nature and treatment of hypochondriasis, which is commonly considered to be an OC spectrum disorder. He served as a consultant on the text revision of the Diagnostic and Statistical Manual of Mental Disorders (DSM-IV-TR), and is a member of the scientific advisory board of the Anxiety Disorders Association of Canada. He has received early career awards from the Canadian Psychological Association, the Association for Advancement of Behavior Therapy, and the Anxiety Disorders Association of America. He is also a Fellow of the Canadian Psychological Association and the Association of Cognitive Therapy. His clinical and research interests include cognitive-behavioral treatments and mechanisms of anxiety disordres and related conditions.

Book preview

Introduction

Probability is how likely something is to occur. Whenever we are uncertain about the outcome of an event, we can quantify the probabilities of particular outcomes. Sometimes it is also used to quantify the likelihood of events that could have happened when it's not known for certain whether they happened. Probability is quantified as a certain number between 0 and 1, where 0 indicates impossibility and 1 certainty of something to happen. The higher the probability of an event indicated there is greater chance that the event will occur.

Probability is a complex and important field of study that is widely used in different scientific areas such as mathematics, finance, computer science, game theory, statistics, physics, gambling, philosophy and artificial intelligence. Probability theory is also used to describe the regularities and underlying mechanics of complex systems. This theory is applied in everyday life in modeling and risk assessment. The markets and insurance industry use probability theory formulas to determine pricing and make various trading decisions. Governments apply the similar method in environmental regulation, financial regulation, and entitlement analysis. In addition to environmental and financial regulations, the probability is also used to analyze trends in biology and ecology.

The best example for understanding probability is something which we are all familiar with. You flip a coin numerous times.  What's the probability that it will turn up tails or heads? In this particular case, there are two possible outcomes. Therefore, the probability of an event is equal to many ways it can happen divided by a total number of possible outcomes. The likelihood of the coin landing on tails or heads is half/half or 50%. You intuitively already know what is the probability in this case, because there are only two possible outcomes and the chances are the same.

P (head and tail ) = 0.5

If we take another example like rolling a dice, there are six different outcomes. If we want to find out what's the probability of rolling a one, following the equation, the number of ways it can happen is divided with a total number of outcomes.  So the probability, in this case, is one/a sixth. We can take another example, and see what's the probability of rolling two numbers a six or a one. Therefore, using an equation the probability, in this case, is two-sixths and one/a third.

The probability of each event to occur when rolling a six-sided dice is

P(rolling a dice) = 1/6

In the next sections of this book, we are going to take a closer look at fundamentals of probability and explanation of permutations and combinations with an example in real-world, the theory of probability in gambling industry as well as real life scenarios where you can apply probability to permutations and combinations.

We are going to mention some possible interpretations of the basic concept of probability. Therefore, after you are done with reading, your view of the world around you will be from another perspective, you will be able to find the logic behind random events as well as to find the probabilities of events which may happen in the future.

History of Probability

The study of probability was developed from mathematics. With the introduction of gambling games and establishment of first land-based casinos, it became apparent that there has been an enormous interest in quantifying the ideas of probabilities. These were beginnings of development, but exact mathematical concepts arose much later. Of course, there are numerous reasons for the slow evolution of the probability theory based on mathematics, but gambling games provided the initial stimulus which was needed.

In the sixteenth century, Gerolamo Cardano Italian mathematician demonstrated the efficiency of determining odds as the ratio of unfavorable to favorable of outcomes. In the seventeenth century, the term 'probable' ,which originated from