Probability in Daily Life

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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 denominator of a probability to the numerator of a probability. For example, if the probability of a horse winning a race is 50 percent (1⁄2), the odds of this horse winning are 2 to 1. COPYRIGHTED MATERIAL

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 can interpret a probability as it applies to an individual or as it applies to a group. Because probabilities stand for long-term percentages (see the previous section), it may be easier to see how they apply to a group rather than to an individual. But sometimes one way makes more sense than the other, depending on the situation you face. The following sections outline ways to interpret probabilities as they apply to groups or individuals so you don’t run into misinterpretation problems.

Playing the instant lottery
Probabilities are based on long-term percentages (over thousands of trials), so when you apply them to a group, the group has to be large enough (the larger the better, but at least 1,500 or so items or individuals) for the probabilities to really apply. Here’s an example...
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