# Lesson 6

Estimating Probabilities Using Simulation

### Lesson Narrative

This lesson introduces the idea of simulation. Different groups of students use different chance experiments that are designed to enable you to approximate the probability of a real world event.

Students follow a process similar to what they used in previous lessons for calculating relative frequencies (the activities in which students were rolling a 1 or 2 on a number cube or drawing a green block out of a bag). The distinction in this lesson is that the outcomes students are tracking are from an experiment designed to represent the outcome of some other experiment that would be harder to study directly. Students see that a simulation depends on the experiment used in the simulation being a reasonable stand-in for the actual experiment of interest (MP4).

This lesson works with estimating the probability of simple events in preparation for students being able to estimate the probability of compound events in upcoming lessons.

### Learning Goals

Teacher Facing

• Comprehend the that term “simulation” (in written and spoken language) refers to a chance experiment used to represent a real-world situation.
• Describe (orally and in writing) a simple chance experiment that could be used to simulate a real-world event.
• Perform a simulation, and use the results to estimate the probability of a simple event in a real-world situation (using words and other representations).

### Student Facing

Let’s simulate real-world situations.

### Required Preparation

Print and cut up slips and spinners from the Diego's Walk blackline master. Provide each group of 3 supplies for 1 type of simulation: choosing a situation slip from a bag, spinning a spinner, or rolling 2 number cubes.  The supplies for each simulation include:

• a paper bag containing a set of slips cut from the blackline master
• a spinner cut from the blackline master, a pencil and a paper clip
• 2 standard number cubes

### Student Facing

• I can simulate a real-world situation using a simple experiment that reflects the probability of the actual event.

Building On

### 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:

• simulation

A simulation is an experiment that is used to estimate the probability of a real-world event.

For example, suppose the weather forecast says there is a 25% chance of rain. We can simulate this situation with a spinner with four equal sections. If the spinner stops on red, it represents rain. If the spinner stops on any other color, it represents no rain.