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
In Part I, you get started with the basics of probability â 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 letâs 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 doesnât sound all that relevant â and it isnât. Thatâs why you wonât see a single âurn problemâ anywhere in this part. However, if you do run across an âurn problemâ in your life, youâll 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
Youâve heard it, thought it, and said it before: âWhat are the odds of that happening?â Someone wins the lottery not once, but twice. You accidentally run into a friend you havenât 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? Thatâs 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 arenât 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 â 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 âodds,â however, isnât 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 (âWhat are my chances of winning the lottery?â), or it can apply to a group (âThe overall percentage of adults who get cancer is âŠâ). You can signify a chance with a percent (80 percent), a proportion (0.80), or a word (such as âlikelyâ). The bottom line of all probability terms is that they revolve around the idea of a long-term chance. When youâre 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; whatâs 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 wonât 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 didnât rain the other 70 percent). So, a 30-percent chance for rain means only that itâs unlikely to rain.
Interpreting probabilities: Thinking large and long-term
