Chapter 1

Probability, Percent, and Rational Numbers

This chapter is about numbers. It is also about a new topic. That topic is called probability. Probability tells us how likely something is to happen.

We start with probability. It helps make math fun. It also helps us remember old skills. Skills like fractions, percents, and decimals.

Fractions, percents, and decimals can look different. But they can mean the same amount. We call this equivalence. Equivalent means "the same value."

We will also learn about statistics. Statistics helps us study information, called data. Probability helps statistics work. That is why we learn probability first.

Doctors use statistics too. They test medicines. They see how well a medicine works. They use percents to share what they learn.

What Is Probability?

Probability is new for you this year. First, we look at things called chance processes. A chance process is something where you don't know what will happen next. Like rolling a die.

We can write probability as a fraction. Or as a decimal. Or as a percent. All of these compare a part to a whole.

All the things that could happen are called a sample space. One single result is called an event.

We can describe an event's probability with words:

• Impossible
• Unlikely
• Equally likely
• Likely
• Certain

Or we can use a number. This number is between 0 and 1.

There are two kinds of probability:

• Experimental probability comes from doing an experiment.
• Theoretical probability comes from thinking about what should happen.

Fractions, Decimals, and Percents

We will also practice fractions, decimals, and percents. We will put them on a number line. This includes positive and negative numbers.

A percent means "per hundred." It is a fraction with 100 on the bottom.

We will use pictures and models to understand percents. We will solve problems with money. Problems about discounts, tips, taxes, and interest.

Probability in Real Life

Probability is all around us!

Weather: If the weather report says 70% chance of rain, should you still go outside? That is a probability question.

Baseball: A batting average tells how often a player gets a hit. If a player's average is .300, that means a 30% chance of getting a hit.

Lottery: Many people buy lottery tickets. They hope to win money. But the chance of winning is very, very small.

The History of Probability

Long ago, in the 1400s, people started studying probability. One story comes from a dice game.

A man named Chevalier de Méré liked to gamble. He played a dice game. He tried to roll a six at least once in four rolls. He won money most of the time.

Then he changed the game. He tried to roll double sixes with two dice. He rolled 24 times. This time, he started losing money!

He didn't know why. So he asked his friend, a mathematician named Blaise Pascal. Pascal worked with another mathematician, Pierre Fermat. Together, they solved the puzzle!

Their work helped start the math of probability that we still use today.

Why did Chevalier de Méré lose?

He thought probabilities always add up. He thought if one roll gives a 1/6 chance, then four rolls give 4/6 chance. But that was wrong!

Pascal figured out that probabilities don't always add. Sometimes, they multiply instead. This helped explain the mistake in the dice game.