Experimental Vs. Theoretical Probability
By Ling Pun
1) Summary
 This lesson plan can be used as extension for Prentice Hall’s Mathematics
Course 3 Chapter 11 Lesson 4.
 Grade 8 mathematics
 Classroom layout (students can be in a group of three with at least one
computer per group)
 Prerequisite knowledge for students (student should have basic knowledge
on representing part of a whole as a fraction, changing fractions to
percent, probability notation, and some experiences on excel)
 Prerequisite knowledge for teachers (for computer: power point and excel,
For math: Bar graph, experimental and theoretical probability, Law of large
numbers, and probability distributions)
 Objectives of the lesson
Students will develop an understanding on distinguishing the difference
between experimental and theoretical probability.
 Time frame for the lesson is 60 minutes
 List of materials (calculators, computers, LCD projector, internet connection,
coins, and number cubes)
 Short description of the content
The focus of this lesson is to compare and contrast experimental
probability and theoretical probability. Several examples will be use to
illustrate the difference between two of them through PowerPoint
presentation. The student group will perform the coin tossing and dice
rolling experiment during the lesson. In addition of the experiments, the
teacher will present an excel simulation that showing how larger number
of trials can lead an experimental probability outcome closer to a
theoretical probability outcome.
 Sunshine State Standards:
 List of key words: Experimental probability, theoretical probability, outcome,
event, random, Law of Large Numbers
2. Lesson plan
 Introduction to the lesson
Many students have a hard time to distinguish the difference between
experimental and theoretical probability. Calculations for probability are
simple and straightforward, but concepts are often abstracted and
confused. This lesson is intended to help students to understand the
difference of the two probabilities and why they are different.
 Teacher-centered approaches:
--Demonstration: teacher will demonstrate how to use the excel
spreadsheet and Hot Potato format quiz.
--Lecture-Discussion: Topics included the following, what is the
relationship between experimental and theoretical probability? Why
they have different result? How can you distinguish the two
probabilities? How does law of Large Number apply to this topic?
--Simulation:
an excel simulation will flip 100- coin when you hit
apple and + to activating the simulation, then you will record how many
heads show up in the data columns in each experiment. The teacher
will perform for five-trial, 10-trial, 20-trial, and 30-trial. Once you
entered all your result, the spreadsheet will calculate each averages
for you. The final step is to graph a bar graph with all five averages
along with the theoretical value (50%). The graph will clearly
demonstrate that when trial increase, the experimental results are
getting closer to the theoretical results.
 Student-centered approaches:
--Cooperative Learning: Students will be in a group of three. They
need to help each other to conduct the coin flipping and dice rolling
experiment, record the results in the worksheet, and create a bar
graph for their experiment results.
--Discussion: They will have a group discussion before the group will
answer teacher’s lecture discussion questions
 Step by step procedure:
The first 10-minute is warn up and review. Teacher must make sure
students know the characteristic of theoretical probability and how to find
the theoretical probability. The vocabulary matching exercise can be used
as bell work as soon as they walk in to the classroom.
The following 40 minutes will be PowerPoint presentation and group
experiments. Three students will conduct the experiment individually and
record the results of the group ( if they do not need to share computer)in the
worksheets. Depending on the actual development for different classes,
teacher can decide whether just one or both experiments will be
proceeding. Teacher needs to make sure that student have enough time to
graph their bar charts.
At the last ten minutes, the teacher will review the quiz answers for
the class and answer questions regarding the lesson martial.
 Description of Class activities:
Bell work (Jmatch activity)
Class work (experiment for coin flipping, dice rolling, and computer
simulations, and an assessment)
 Including instructional strategies to be used:
Teacher will guide students to connect the results from experiments
and simulations to their topic study.
 Closure to the lesson:
The review will include compare and contract of experimental verse
theoretical probability. And why do we need to know the difference to really
understand the essences of probability.
 Assessments
I used Hot Potato to create a quiz for this lesson. The entire quiz is
closely reflected the materials used for the lesson. It is in multiple-choice
format so that students can analyze the answers before making their
decisions.
I also have a paper quiz for this lesson, and that can be given the next
day as extension or homework for the lesson.
 Self-assessment:
I will make the necessary changes, after this lesson has been used in
my classes
Assessment (Hot Potato Quiz)
Answer the following questions according the materials covered in this
lesson
1) What is probability?
(A number from 0 to 1 that tells you how likely something is to happen.)
2) You toss two pennies 20 times P (2 heads) = 3/20. Identify the probability
(Experimental probability)
3) A spinner is divided into six equal sections. Three sections are green and three
sections are blue. P (green) is ½. Identify the probability
(Theoretical probability)
4) In a survey, 50 people were asked to pick which movie they would see this
weekend. Ten people chose Dead Man’s Chest. What is the experimental probability of
someone wanting to see Dead Man’s Chest?
(1/5)
5) A number cube is tossed 20 times and lands on 1 two times and on 5 four times.
Find the experimental probability of not landing on 1.
(9/10)
6) Suppose you select a number at random from a bag that contains a 1, 2, 3,4, 5, 6. What
is the theoretical probability that you will pick a integer?
(1)
7) Compare Experimental and Theoretical probability
(Both probabilities are ratios that compare the number of favorable outcomes to the total
number of possible outcomes)
8) Contrast Experimental and Theoretical probability
(Experimental probability is the result of an experiment. Theoretical probability is what is
expected to happen.)
9) Why an experimental probability outcome will close to a theoretical outcome
the experiments are repeated many times?
(Law of Large Numbers)
10) Give an example of a random outcome
(Rolling a dice and get the number 5)
when