Probability For Dummies

Deborah J. Rumsey

• Publisher: For Dummies
• Year: 2018
• ISBN:
  9781118429099
• Edition: 1
• Topic: Mathematik
• Subtopic: Wahrscheinlichkeitsrechnung & Statistiken

Packed with practical tips and techniques for solving probability problems
Increase your chances of acing that probability exam -- or winning at the casino! Whether you're hitting the books for a probability or statistics course or hitting the tables at a casino, working out probabilities can be problematic. This book helps you even the odds. Using easy-to-understand explanations and examples, it demystifies probability -- and even offers savvy tips to boost your chances of gambling success! Discover how to
* Conquer combinations and permutations
* Understand probability models from binomial to exponential
* Make good decisions using probability
* Play the odds in poker, roulette, and other games

Part I

The Certainty of Uncertainty: Probability Basics

In this part …

In Part I, you get started with the basics of probability — the terminology, the basic ideas of finding a probability, and, perhaps most importantly, how to organize and set up all the information you have in order to successfully calculate a probability. You also discover ways in which people use probability in the real world.

But let’s be honest. When it comes to a class that involves probability, is there truly a real world? Maybe, maybe not. Counting the number of ways to pick three green balls and four red balls from an urn that contains twenty green balls and thirty red balls doesn’t sound all that relevant — and it isn’t. That’s why you won’t see a single “urn problem” anywhere in this part. However, if you do run across an “urn problem” in your life, you’ll know how to answer it, using the techniques from Part I.

Chapter 1

The Probability in Everyday Life

In This Chapter

Recognizing the prevalence and impact of probability in your everyday life

Taking different approaches to finding probabilities

Steering clear of common probability misconceptions

You’ve heard it, thought it, and said it before: “What are the odds of that happening?” Someone wins the lottery not once, but twice. You accidentally run into a friend you haven’t seen since high school during a vacation in Florida. A cop pulls you over the one time you forget to put your seatbelt on. And you wonder … what are the odds of this happening? That’s what this book is about: figuring, interpreting, and understanding how to quantify the random phenomena of life. But it also helps you realize the limitations of probability and why probabilities can take you only so far.

In this chapter, you observe the impact of probability on your everyday life and some of the ways people come up with probabilities. You also find out that with probability, situations aren’t always what they seem.

Figuring Out what Probability Means

Probabilities come in many different disguises. Some of the terms people use for probability are chance, likelihood, odds, percentage, and proportion. But the basic definition of probability is the long-term chance that a certain outcome will occur from some random process. A probability is a number between zero and one — a proportion, in other words. You can write it as a percentage, because people like to talk about probability as a percentage chance, or you can put it in the form of odds. The term “odds,” however, isn’t exactly the same as probability. Odds refers to the ratio of the probability of an event happening to the probability of the event not happening. For example, if the probability of a horse winning a race is 50 percent (

), the odds of this horse winning are

. So the odds are 1 to 1.

Understanding the concept of chance

The term chance can take on many meanings. It can apply to an individual (“What are my chances of winning the lottery?”), or it can apply to a group (“The overall percentage of adults who get cancer is …”). You can signify a chance with a percent (80 percent), a proportion (0.80), or a word (such as “likely”). The bottom line of all probability terms is that they revolve around the idea of a long-term chance. When you’re looking at a random process (and most occurrences in the world are the results of random processes for which the outcomes are never certain), you know that certain outcomes can happen, and you often weigh those outcomes in your mind. It all comes down to long-term chance; what’s the chance that this or that outcome is going to occur in the long term (or over many individuals)?

If the chance of rain tomorrow is 30 percent, does that mean it won’t rain because the chance is less than 50 percent? No. If the chance of rain is 30 percent, a meteorologist has looked at many days with similar conditions as tomorrow, and it rained on 30 percent of those days (and didn’t rain the other 70 percent). So, a 30-percent chance for rain means only that it’s unlikely to rain.

Interpreting probabilities: Thinking large and long-term

You ...