# Lesson 2: Chance Experiments

Let’s investigate chance.

## 2.1: Which is More Likely?

Which is more likely to happen?

1. When reaching into a dark closet and pulling out one shoe from a pile of 20 pairs of shoes, you pull out a left shoe.

2. When listening to a playlist—which has 5 songs on it—in shuffle mode, the first song on the playlist plays first.

## 2.2: How Likely Is It?

1. Label each event with one of these options:

impossible,   unlikely,   equally likely as not,   likely,   certain

1. You will win grand prize in a raffle if you purchased 2 out of the 100 tickets.
2. You will wait less than 10 minutes before ordering at a fast food restaurant.
3. You will get an even number when you roll a standard number cube.
4. A four-year-old child is over 6 feet tall.
5. No one in your class will be late to class next week.
6. The next baby born at a hospital will be a boy.
1. It will snow at our school on July 1.
2. The sun will set today before 11:00 p.m.
3. Spinning this spinner will result in green.
4. Spinning this spinner will result in yellow.

2. Discuss your answers to the previous question with your partner. If you disagree, work to reach an agreement.

3. Invent another situation for each label, for a total of 5 more events.

## 2.3: Take a Chance

This applet displays a random number from 1 to 6, like a number cube. With a partner, you will play a game of chance.

• In the first round, one of you will score on an even roll and one of you will score on an odd roll. You decide that first.

• In the second round, the winner of round one will score on numbers $1 - 4$, and the other player will score on numbers $5 - 6$.

• Each round is ten rolls. Be sure to turn on "History" after your first roll and wait for it to update before rolling again.

GeoGebra Applet pbczUxkY

1. When each player had three numbers, did one of them usually win?
2. When one player had four numbers, did you expect them to usually win? Explain your reasoning.

## 2.4: Card Sort: Likelihood

1. Your teacher will give you some cards that describe events. Order the events from least likely to most likely.

2. After ordering the first set of cards, pause here so your teacher can review your work. Then, your teacher will give you a second set of cards.

3. Add the new set of cards to the first set so that all of the cards are ordered from least likely to most likely.

## Summary

A chance experiment is something that happens where the outcome is unknown. For example, if we flip a coin, we don’t know if the result will be a head or a tail. An outcome of a chance experiment is something that can happen when you do a chance experiment. For example, when you flip a coin, one possible outcome is that you will get a head. An event is a set of one or more outcomes.

We can describe events using these phrases:

• Impossible
• Unlikely
• Equally likely as not
• Likely
• Certain

For example, if you flip a coin:

• It is impossible that the coin will turn into a bottle of ketchup.
• It is unlikely the coin will land on its edge.
• It is equally likely as not that you will get a tail.
• It is likely that you will get a head or a tail.
• It is certain that the coin will land somewhere.

The probability of an event is a measure of the likelihood that an event will occur. We will learn more about probabilities in the lessons to come.

## Glossary

event

#### event

An event is a set of possible outcomes of a chance experiment. It could be just a single outcome, like heads when you toss a coin, or it could be a set of outcomes. For example, when you perform the chance experiment of tossing a coin twice, then "at least one head" is an event that includes the outcomes heads-tails, tails-heads, and heads-heads.

outcome

#### outcome

An outcome of a chance experiment is one of the things that can happen when you do the experiment. For example, the possible outcomes of tossing a coin are heads and tails.

chance experiment

#### chance experiment

A chance experiment is something you can do over and over again and you don't necessarily know what is going to happen each time. For example, tossing a coin is a chance experiment which could result in heads or tails.