The Everything Everyday Math Book

From Tipping to Taxes, All the Real-World, Everyday Math Skills You Need

Christopher Monahan

• Editore: Everything
• Anno: 2013
• ISBN:
  9781440566448
• Argomento: Matematica
• Categoria: Riferimenti matematici

All the math basics you'll ever need! It's not too late to learn practical math skills! You may not need to use quadratic equations very often, but math does play a large part in everyday life. On any given day, you'll need to know how long a drive will take, what to tip a waiter, how large a rug to buy, and how to calculate a discount. With The Everything Everyday Math Book, you'll get a refresher course in all the basics you need, including:

• Adding and subtracting fractions
• Understanding percentages
• Using ratios
• Finding area and perimeter

You'll the learn formulas and shortcuts to help in hundreds of everyday situations, from budgeting and paying bills to shopping, redecorating, preparing taxes, and evaluating loans and other financial instruments. With this easy-to-follow guide, you'll never get stuck on a math problem again!

CHAPTER 15
Probability and Statistics

Desktop computers have had a tremendous impact on the world, especially by boosting people’s ability to collect data. Once data are collected, however, they have to be analyzed—a process so important that the phrase data-driven decisions (or some variation of it, such as data-based marketing) is used in every industry. Much of the time, to make an informed decision about how to interpret data, you have to consider statistics. Statistics has two branches. Descriptive statistics yields information about the center and spread of data. (You will learn more about these two concepts in the discussion to come.) Inferential statistics, the application of probability theory, is a tool used to make data-driven decisions. The most basic elements of probability and statistics are learning how to count and determining where the center of your data is located.

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More and more businesses and educational programs have adopted the policy of data-driven decisions. The questions “Are the data accurate?” and “Who is interpreting the data?” have always been asked and will continue to be asked.

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Simple Events—Flipping a Coin

In the language of probability, a simple event is an event in which one outcome is examined. For instance, flipping a coin, rolling a die, spinning a spinner, drawing a ticket from a hat for a 50-50 drawing, and playing a number at a roulette table are all simple events. (In a 50-50 drawing, the winner takes half of the pot, and the sponsoring organization takes the other half. Such drawings are popular as fundraisers for charities.) Before you continue learning about simple events—and probability in general—there is some language that you should be familiar with.

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The study of probability did not begin until the mid 17th century when Blaise Pascal and Pierre de Fermat were asked to examine a problem about gambling.

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The Language of Probability

• Probability is the relative frequency with which an event will occur. In simpler language, probability is the ratio of the number of ways a particular event can occur to the number of ways all possible events can occur.
• A fair event is one in which all possible events have the same chance of occurring, whereas in a biased event, some outcomes are more likely than others. (You may have heard of “loaded dice” being used to cheat in gambling. Loaded dice have been altered so that certain numbers are more likely to occur than others.)

Flip a fair coin. The probability that it will show Heads is

.

Roll a fair die. The probability that the die will show a 5 is

.

Draw a ticket from a hat for a 50-50 drawing. The probability that you will win depends on two factors: how many tickets were sold and how many you bought. If 250 tickets were sold for the drawing and you bought 1 ticket, the probability that you will win is

. However, if you bought 25 tickets, your chance of winning increases to

, or

.

Compound Events—Rolling the Dice

Computing probabilities for events that require more than one outcome to occur (such as getting the coin to land showing Heads and rolling a 5 when you toss a die) is more complicated. The Fundamental Theorem of Counting (fundamental in the sense of “bas...