# Lesson 3

What Are Probabilities?

### Lesson Narrative

In this lesson students begin to assign probabilities to chance events. They understand that the greater the probability, the more likely the event will occur. They define an outcome as a possible result for a chance experiment. They learn that the sample space is the set of all possible outcomes, and understand that a process is called random when the outcome of an experiment is based on chance. They reason that if there are $$n$$ equally likely outcomes for a chance experiment, they construct the argument (MP3) that the probability of each of these outcomes is $$\frac{1}{n}$$.

In future lessons students will be asked to design and use simulations. Each lesson leading up to that helps prepare students by giving them hands-on experience with different types of chance experiments they could choose to use in their simulations. In this lesson students work with drawing paper slips out of a bag.

### Learning Goals

Teacher Facing

• Generalize (orally) the relationship between the probability of an event and the number of possible outcomes in the sample space, for an experiment in which each outcome in the sample space is equally likely.
• List (in writing) the sample space of a simple chance experiment.
• Use the sample space to determine the probability of an event, and express it as a fraction, decimal, or percentage.

### Student Facing

Let’s find out what's possible.

### Required Preparation

Print and cut up slips from the What's in the Bag? blackline master. One copy is needed for every 4 students. Each set of slips should be put into a paper bag.

### Student Facing

• I can use the sample space to calculate the probability of an event when all outcomes are equally likely.
• I can write out the sample space for a simple chance experiment.

### Glossary Entries

• chance experiment

A chance experiment is something you can do over and over again, and you don’t know what will happen each time.

For example, each time you spin the spinner, it could land on red, yellow, blue, or green.

• event

An event is a set of one or more outcomes in a chance experiment. For example, if we roll a number cube, there are six possible outcomes.

Examples of events are “rolling a number less than 3,” “rolling an even number,” or “rolling a 5.”

• 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.

• probability

The probability of an event is a number that tells how likely it is to happen. A probability of 1 means the event will always happen. A probability of 0 means the event will never happen.

For example, the probability of selecting a moon block at random from this bag is $$\frac45$$.

• random

Outcomes of a chance experiment are random if they are all equally likely to happen.

• sample space

The sample space is the list of every possible outcome for a chance experiment.

For example, the sample space for tossing two coins is: