7.SP.6: Approximate the probability of a chance event by collecting data on the
chance process that produces it and observing is long-run relative frequency,
and predict the approximate relative frequency given the probability.
7.SP.7: Develop a probability model and use it to find probabilities of events.
Compare probabilities from a model to observed frequencies; if the agreement
is not good, explain possible sources of the discrepancy.
a. Develop a uniform probability model by assigning equal probability to all
outcomes, and use the model to determine probabilities of events.
7.SP.8: Find the probabilities of compound events using organized lists, tables, tree
diagrams, and simulation.
c. Design and use a simulation to generate frequencies for compound events.
7.5.10 & 11: Using Simulation to Estimate a Probability

Students learn simulation as a method for estimating probabilities that can be
used for problems in which it is difficult to collect data by experimentation or by
developing theoretical probability models.

Students learn how to perform simulations to estimate probabilities.

Students use various devices to perform simulations (eg: coin, number cube,
cards.)

Students compare estimated probabilities from simulations to theoretical
probabilities.
WKSP
HW
Media
Student Learning Goal
CC
Lesson
Standard
Pre Requisite
Simulation
#103
Spiral Review #27
Simulation
Simulate:
Outcomes
Example: Families
Suppose that a family has three children. Let’s brainstorm what can be used to simulate
the genders of the children:




Coin
Die
Playing Card

Note Card

Colored Disk

Random Number Generator
Spinner
Say we chose to use three coins to represent the children of a family. Each set of three
tosses is called a ________.
 A trial is considered to be a _________ if you get what you want.
 A trial is considered to be a _________ if you don’t get what you want.
Let’s say we are looking for the probability of the birth of all the children in a family
being the same. What two outcomes would be considered a success?
Any other outcome would be considered a __________.
The following represents the outcomes of 50 trials of tossing a fair coin three times per
trial. Use H to represent a boy birth and T to represent a girl birth.
P (three boys or three girls) =
P (at least 1 girl) =
Let’s compare these experimental results with theoretical results.
P (three boys or three girls) =
P (at least 1 girl) =
What should we do to make the experimental results closer to the theoretical results?
Simulation
Exercise
1. Suppose that, on average, a basketball player makes about three out of every four
foul shots. In other words, she has a 75% chance of making each foul shot she
takes. A numbered cube is used to represent the basketball player’s ability as
follows:
Success: rolling a 1, 2 or 3
Failure: rolling a 4
(If a 5 or 6 is rolled, it is to be ignored!)
Based on the following 50 trials of rolling a fair number cube, find an estimate of
the probability that she makes five or six of the six foul shots she takes.
2. Using colored disks, describe how one at-bat could be simulated for a baseball
player who has a batting average of 0.300. Note that a batting average of 0.300
means the player gets a hit (on average) three times out of every ten times at bat.
Be sure to state clearly what the color represents.
3. What might be a good way to generate outcomes for a birth-month problem: use
coins, number cubes, cards, spinners, colored disks, or random numbers?
How would you simulate one trial of seven birth months?
How is the simulated estimate determined for the probability that at least two
people in a group of seven people were born in the same month?
Simulation
Name: __________________________________
Pre-Algebra
Date: ______
Exit Ticket
A mouse is placed at the start of the maze shown below. If it reaches station B, it is
given a reward. At each point where the mouse has to decide which direction to go,
assume that it is equally likely to go in either direction. At each decision point 1, 2, 3, it
must decide whether to go left (L) or right (R). It cannot go backwards.
a. The following questions are based on the theoretical model:

List the possible paths of a sample space for the paths the mouse can take.

P (terminal A) =
P (terminal B) =
P (terminal C) =
b. Based on the following set of simulated paths,
estimate the probabilities that the mouse arrives at the following terminals:
P (A) =
P (B) =
P (C) =
Simulation
Name: _______________________________________
Pre-Algebra
Date: _____
HW #103
Lesson Summary

Simulation is a method that uses an artificial process (like tossing a coin or rolling a number cube) to
represent the outcomes of a real process that provides information about the probability of events.

Design a Simulation:
1.
Identify possible outcomes then decide how to simulate them (coin, number cube, (note) card, spinner,
colored disks, random number generator, etc.)
2.
Specify what a trial for the simulation will look like and what define what a success and a failure would
be.
3.
Make sure you carry out enough trials to ensure that the estimated probability gets closer to the actual
probability. AKA – the relative frequency must level off.
Suppose that a dartboard is made up of the 8x8 grid of squares shown below. Also,
suppose that when a dart is thrown, it is equally likely to land on any one of the 64
squares. A point is won if the dart lands on one of the 16 black squares. Zero points are
earned if the dart lands in a white square.
1.
For one throw of a dart, what is the probability of winning a point if the dart lands
on a black square?
2.
Lin wants to use a number cube to simulate the result of one dart. She suggests
that 1 on a number cube could represent a win. Getting 2, 3 or 4 could represent
no point scored. She says that she would ignore getting a 5 or 6. Is Lin’s
suggestion for a simulation appropriate?
Simulation
3. Suppose a game consists of throwing a dart three times. A trial consists of three
rolls of the number cube. Based on Lin’s suggestion in question #2 and the
following simulated rolls, estimate the probability of scoring two points in three
darts.
4. The theoretical probability model for winning 0, 1, 2 and 3 points in three throws of
the dart as described in this problem is:

Winning 0 points has a probability of 0.42;

Winning 1 points has a probability of 0.42;

Winning 2 points has a probability of 0.14;

Winning 3 points has a probability of 0.02.
Use the simulated rolls in question #3 to build a model of winning 0, 1, 2 and 3
points, and compare it to the theoretical model.