Standard
7.5.8: The Difference Between Theoretical Probabilities and Estimated Probabilities
7.5.9: Comparing Estimated Probabilities to Probabilities Predicted by a Model
Given theoretical probabilities based on a chance experiment, students describe
what they expect to see when they observe many outcomes of the experiment.

Students distinguish between theoretical probabilities and estimated
probabilities.

Students understand that probabilities can be estimated based on observing
outcomes of a chance experiment.
http://www.rossmanchance.com/applets/CoinTossing/CoinToss.html
coin applet
#102
Spiral Review #27
WKSP
Media

HW
Student Learning
Goal
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.
b. Develop a probability model (which may not be uniform) by observing
frequencies in data generated from a chance process.
CC
Lesson
Pre Requisite
Theoretical vs. Estimated
Theoretical vs. Estimated
When flipping a coin, what is the probability of the coin landing on tails?
Theoretical Probability:
Law of Large Numbers
Example: Coin
A coin is tossed (http://www.rossmanchance.com/applets/CoinTossing/CoinToss.html).
You then record the probability of getting a tails up to the most recent trial.
Toss Tails Relative Frequency
Of Tails
1
2
3
4
5
Toss Tails Relative Frequency
Of Tails
10
15
20
25
30
Tails
Graph the results of this experiment.
What relative frequency of tails do you think this graph is approaching?
Experimental / Estimated / Empirical Probability:
Beth taped 10 pennies together to form a small stack. The top penny of her stack
showed heads and the bottom penny showed tails. Do you think the probability of
tossing tails from the stack is the same as getting a tails from a coin? Explain.
Theoretical vs. Estimated
Exercise
1. Which of the following graphs would represent the relative frequencies of heads
when tossing a penny?
2. Jerry indicated that after tossing a penny 30 times, the relative frequency of heads
was 0.47 (to the nearest hundredth). He indicated that after 31 times, the relative
frequency of heads was 0.55. Are Jerry’s summaries possible? Explain.
3. Jerry observed 5 heads in 100 tosses of his coin. Do you think this was a fair coin?
Why or why not?
Guess how many
Example: Blue Marbles
We’re going to play a game. 10 marbles have been placed into a bag. Without peeking,
I’d like for you to guess how many marbles are blue.
Trial
1
2
3
4
5
6-10
11-15
16-20
21-25
26-30
Number of Relative Frequency
Blue Marbles
of Blue Marbles
Guess how many
blue marbles are
in the bag.
Theoretical vs. Estimated
Name: __________________________________
Pre-Algebra
Date: ______
Exit Ticket
Theoretical vs. Estimated
Name: _______________________________________
Pre-Algebra
Date: _____
HW #102
Lesson Summary

The long-run relative frequency of a chance experiment approaches the theoretical probability of the event.
1. Look at the spinner.
Which tally chart shows the most likely results of 30 spins?
2.
There is one red chip and one blue chip in a bag. Taralynn randomly draws out a
chip and then replaces it. She repeats the process 10 times. Separately, a
computer generates 300 random draws. The two sets of data are shown here:
a. For each set of results, compare the total number of blue chips drawn to the
mathematical probability of drawing a blue chip.
b. Were Taralynn’s results OR the computer’s results closer to the mathematical
expectations?
Theoretical vs. Estimated
Review:
3. In the seventh grade class of 28 students, there are 16 girls and 12 boys. If one
student is randomly chosen to win a prize, what is the probability that a girl is
chosen?
4. A sponsor of a 5K run/walk for charity wishes to create a stamp of its billboard to
commemorate the event. If the sponsor uses a scale where 1 inch represents 4
feet, and the billboard is a rectangle with a width of 14 feet and a length of 48 feet,
what will be the shape and size of the stamp?