# Lesson 5

More Estimating Probabilities

### Lesson Narrative

In this lesson students compare the results from running actual trials of an experiment to the expected, calculated probabilities. They also use their data to see that additional trials usually produce more accurate results as minor differences even out after many trials.

In the first activity, students spin four different spinners to see that the outcomes in a sample space may not be equally likely, and they examine the spinners to construct arguments (MP3) about why some outcomes are more likely than others. In the next activity, students draw blocks out of a bag repeatedly and use the relative frequency to estimate the probability of getting a green block (MP8). This activity differs from the activity in the previous lesson where students were rolling a number cube repeatedly because in this lesson the students do not know the probability of getting a green block before they start the experiment.

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 spinners and drawing blocks out of a bag.

### Learning Goals

Teacher Facing

• Describe (orally and in writing) reasons why the relative frequency from an experiment may not exactly match the actual probability of the event.
• Recognize that sometimes the outcomes in a sample space are not equally likely.
• Use the results from a repeated experiment to estimate the probability of an event, and justify (orally and in writing) the estimate.

### Student Facing

Let’s estimate some probabilities.

### Required Preparation

Provide 1 set of 4 spinners cut from the Making My Head Spin blackline master for every 4 students. Each student will need a pencil and paper clip to use with the spinners.

For the How Much Green activity, prepare a paper bag containing 5 snap cubes (3 green and 2 of another matching color) for every 3–4 students.

### Student Facing

• I can calculate the probability of an event when the outcomes in the sample space are not equally likely.
• I can explain why results from repeating an experiment may not exactly match the expected probability for an event.

### 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: