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Grade 8 • Unit 15: Probability

LESSON 15.2
Experimental Probability
Table of Contents

Learning Competency 1
Learning Objectives 1
Essential Questions 2
Prerequisite Skills and Topics 2
Lesson Proper 3
A. Introduction to the Lesson 3
B. Discussion 5
C. Practice & Feedback 10
Performance Assessment 17
Worksheet Answer Key 18
Synthesis 20
Bibliography 21
 Grade 8 • Unit 15: Probability

Unit 15 | Probability

Lesson 2: Experimental Probability

Learning Competency
At the end of the lesson, the learners should be able to illustrate an
experimental probability and a theoretical probability (M8GE-IVi-1).

Learning Objectives
At the end of this lesson, the learners should be able to do the following:

• Differentiate experimental from theoretical probability.

• Solve the experimental probability of simple events.

• Compare the experimental and theoretical probability of a simple event.

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 Grade 8 • Unit 15: Probability

Essential Questions

At the end of this lesson, the student should be able to answer the following questions:
● What situations make use of experimental probability but not theoretical
probability?
● What are the limitations of theoretical probability which make us use experimental
probability?

Prerequisite Skills and Topics

Skills:
● Comparing rational numbers
● Finding the probability of simple events

Topics:
● Math 7 Unit 3: Rational Numbers | Lesson 4: Operations on Rational Numbers
● Math 8 Unit 15: Simple Events | Lesson 1: Probability of Simple Events

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 Grade 8 • Unit 15: Probability

Lesson Proper

A. Introduction to the Lesson

Suggested Warm-up Activities
Choose from any of the following warm-up activities. These warm-up activities should
either stimulate recall of the previous lesson or introduce the lesson and not already
used in the study guide.

Activity 1: Event Planner

This activity will help the students recall how to compute the probability of simple
events.

Duration: 10 minutes

Materials Needed: pen and paper

Methodology:
1. Instruct the students to create a question that asks for the probability of any
simple event based on the given experiment.
Consider the following experiments.
a. Slips of paper are numbered from 1 to 15. One piece of paper is to be
picked at random.
b. A die is rolled.
c. A box contains 4 red, 5 blue, 8 yellow, and 2 green marbles. One marble is
to be picked at random.
2. Call random students that will create questions and ask his/her classmate to
answer.
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 Grade 8 • Unit 15: Probability

Expected Results:
Students should be able to create and answer questions on probability based on the
given experiment.

Guide Questions:
1. How do we compute for the probability of a simple event?
2. Do we need to conduct an experiment before we get its probability? Why or
why not?

Activity 2: Experiment vs. Theory

This activity will help the students differentiate experimental and theoretical
probability.

Duration: 10 minutes

Materials Needed: die, bowl with 5 numbers on slips of paper, coin

Methodology:
1. Divide the students into groups with six members each.
2. Ask each group to compute for the probability of each event in the following
experiment and compare whether each event has equal probabilities.
a. rolling a die
b. picking a number in a bowl
c. tossing a coin
3. Ask each group to verify the computed probabilities by conducting the
experiment and repeating the activity ten times.
4. Instruct each group to record the result and compare it to the probability
they computed in the previous step. Ask the guide questions below.

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 Grade 8 • Unit 15: Probability

Expected Results:
Each group should be able to compute the theoretical probability of each experiment.
1
a. Each face of a die has a probability of 6.
1
b. Each number in the bowl has a probability of 5.
1
c. Each side of the coin has a probability of 2.

Likewise, each group should be able to compare the result of the actual experiment
to the probability of each event in each experiment.

Guide Questions:
1. How will you compare the result of the actual experiment to the probability
that you computed? Are they the same? Why or why not?
2. Does theoretical probability make a good prediction based on the result of
each experiment?
3. What type of probability is based on the result of the actual experiment?

Teacher’s Notes
To help better gauge students’ readiness for this lesson, you may assign the short test
given in the Test Your Prerequisite Skills section of the corresponding study guide.

B. Discussion

1. Define and Discover

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 Grade 8 • Unit 15: Probability

Teacher’s Notes
You may use the Learn about It! slides in the presentation file to discuss the following
key concepts and examples. Make sure to address student questions before jumping
from one concept to another.

● Experiment – process of repeating an activity whose outcomes are limited to

well-defined choices

Example:
Flipping a coin is an example of an experiment.

● Sample Space – set of well-defined possible outcomes or choices in a

statistical experiment

Example:
The sample space in flipping a coin is {Heads, Tails}.

● Theoretical Probability – probability that relies on the total number of

possible successes relative to the total number of possible outcomes.

Example:
1
The probability of getting a head in flipping a coin is .
2

● Experimental Probability – the probability that relies on the actual result of

an experiment; it is the ratio of the number of times an event actually occurs
to the total number of times the activity is repeated.

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 Grade 8 • Unit 15: Probability

No. times the event actually occurs

Experimental Probability =
No. of times the activity is repeated

Example:
A coin is tossed five times, and the tail turns four times. What is the
experimental probability of a tail turning?

To find the experimental probability, we need to determine the number of

times a tail turns and the total number of tosses. Based on the problem, the
tail turns 4 times out of 5 trials. Thus, the experimental probability of a tail
turning is
No. times the event actually occurs
Experimental Probability =
No. of times the activity is repeated
4
=
5

Note that experimental probability differs from theoretical probability. In

theoretical probability, there is no actual result recorded in an experiment but
only relies on theory and facts.

2. Develop and Demonstrate

Example 1
A coin is tossed 15 times. The results are shown below. What is the experimental
probability of a tail turning?

H H T T H
T H T T H
H T H H H

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 Grade 8 • Unit 15: Probability

Solution:
1. Determine the number of times the tail turns up and the number of times the
activity is repeated.

H H T T H
T H T T H
H T H H H

Tail turns up 6 times, and the activity is repeated 15 times.

2. Compute the experimental probability.

No. times the event actually occurs

EP =
No. of times the activity is repeated
6
𝐸𝑃(Tail) =
15
2
=
5

𝟐
Thus, the experimental probability of a tail turning is 𝟓.

Example 2
A spinner with four congruent wedges of different colors is spun several times. The
frequency of the result is given below. What is the experimental probability of the
pointer pointing on the red wedge?

Color Frequency
Red 12
Blue 7

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 Grade 8 • Unit 15: Probability

Yellow 10
Green 15

Solution:
1. Determine the number of times the pointer points on the red wedge and the
number of times the spinner is spun.

Based on the frequency table, the pointer points on the red wedge 12 times. To
find the number of times the spinner is spun, we need to add the frequencies.

Total spins = 12 + 7 + 10 + 15
= 44

2. Compute the experimental probability.

No. times the event actually occurs

EP =
No. of times the activity is repeated
12
𝐸𝑃(Red) =
44
3
=
11

𝟑
Thus, the experimental probability of the pointer pointing on the red wedge is 𝟏𝟏.

Example 3
An archer wants to know the likelihood of hitting the target. Out of 400 attempts, he
hit the target 350 times. What is the experimental probability that he will miss the
target on the next attempt?

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 Grade 8 • Unit 15: Probability

Solution:
1. Determine the number of times the archer missed the target and the total number
of attempts.

The archer has a total of 400 attempts. He hit the target 350 times. Thus, he missed
the target 50 times.

2. Compute the experimental probability.

No. times the event actually occurs

EP =
No. of times the activity is repeated
50
𝐸𝑃(Miss) =
400
1
=
8

Thus, the experimental probability that the archer will miss the target on the next
𝟏
attempt is .
𝟖

C. Practice & Feedback

For Individual Practice
1. Ask the students to answer the following problem items individually using pen
and paper.
2. Give students enough time to answer the problem items.
3. Call a random student to show his or her work on the board afterward.
4. Let the student share how he or she comes up with his or her solution.
5. Inform the student the accuracy of his answer and solution, and in the case
when there is some sort of misconception, lead the student to the right
direction to find the correct answer.

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 Grade 8 • Unit 15: Probability

Problem 1
A basketball player attempted 12 free throws. The result of each attempt is as
follows:

missed shoot shoot shoot

missed missed shoot shoot
shoot shoot missed missed

What is the experimental probability that the basketball player will shoot the next free
throw?

Solution:
1. Determine the number of times that the basketball player shoots the ball and
the total number of free throws.

missed shoot shoot shoot

missed missed shoot shoot
shoot shoot missed missed

The basketball player shoots the ball 7 times out of 12 free throws.

2. Compute the experimental probability.

No. times the event actually occurs

EP =
No. of times the activity is repeated
7
𝐸𝑃(Shoot) =
12

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 Grade 8 • Unit 15: Probability

Thus, the experimental probability that the basketball player will shoot the next free
𝟕
throw is 𝟏𝟐.

Problem 2
The table below shows the number of times each face of a die shows up when
rolled.

Number Frequency
1 7
2 12
3 5
4 9
5 15
6 13

What is the experimental probability of a number greater than 4 to show up?

Solution:
1. Determine the number of times a number greater than 4 shows up and the total
number of rolls.

To find the total number of rolls, we add all the frequencies.

Total rolls = 7 + 12 + 5 + 9 + 15 + 13
= 61

To find the number of times a number greater than 4 shows up, we add the
frequencies of 5 and 6. Thus, 15 + 13 = 28.

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 Grade 8 • Unit 15: Probability

2. Compute the experimental probability.

No. times the event actually occurs

EP =
No. of times the activity is repeated
28
𝐸𝑃(> 4) =
61

𝟐𝟖
Thus, the experimental probability of a number greater than 4 showing up is .
𝟔𝟏

Problem 3
The scores below show the number of goals a certain soccer team makes in the first
round of eliminations.

2, 2, 3, 4, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1

What is the experimental probability that the team will score at least two goals in the
next game?

Solution:
1. Determine the number of games that the team scored at least two goals and the
total number of games.

Based on the given data, the team scored at least two goals in 6 games. These are
2, 2, 3, 4, 2, 2. The team played 14 games, 8 of which they scored only one goal.

2. Compute the experimental probability.

No. times the event actually occurs

EP =
No. of times the activity is repeated

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 Grade 8 • Unit 15: Probability

6 3
𝐸𝑃(≥ 2 goals) = =
14 7

Thus, the experimental probability that the team will score at least two goals in the
𝟑
next game is 𝟕.

For Group Practice

1. Ask the students to form a minimum of two groups to a maximum of five groups.
2. Each group will answer problem items 4 and 5. These questions are meant to test
students’ higher-order thinking skills by working collaboratively with their peers.
3. Give students enough time to analyze the problem and work on their solution.
4. Ask each group to assign a representative to show their solution on the board and
discuss as a group how they come up with their solution.
5. Inform the student the accuracy of his answer and solution, and in the case when
there is some sort of misconception, give the student opportunity to work with
his/her peers to re-analyze the problem, and then lead them to the right direction
to find the correct answer.

Problem 4
Out of 12 quizzes, Francis passed the 1st, 2nd, 5th, and 9th quiz. Compare the
theoretical and experimental probability that Francis will pass the next test.

Solution:
1. Compute the theoretical probability.

The theoretical probability of simple events is given by:

No. of times an event occurs

P(E) =
total number of possible outcomes
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 Grade 8 • Unit 15: Probability

In a test, a person can either pass or fail it. Thus, the probability that Francis will
pass the next quiz is:

1
𝑃(Pass) =
2

2. Compute the experimental probability.

Based on the problem, Francis passed the 1st, 2nd, 5th, and 9th quiz. Thus, he
passed the 4 quizzes out of 12. The experimental probability that he will pass the
next quiz is:

No. times the event actually occurs

EP =
No. of times the activity is repeated
4
𝐸𝑃(Pass) =
12
1
=
3

3. Compare the probabilities.

1 1
The theoretical probability is 2, while the experimental probability is 3.

1 1
>
2 3

Therefore, the theoretical probability that Francis will pass the next quiz is
greater than its experimental probability.

Problem 5
A manufacturer can make 10 000 watches a month. Two hundred watches were
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 Grade 8 • Unit 15: Probability

tested to determine the quality of the products, and it was found that 20 were
defective. What is the best estimate of the number of quality watches the
manufacturer could make each month?

Solution:
1. Determine the number of quality watches out of the total number tested.

The manufacturer found out that 20 watches are defective out of 200. Thus,
there are 180 quality watches that are free of defects.

2. Compute the experimental probability.

No. times the event actually occurs

EP =
No. of times the activity is repeated
180
𝐸𝑃(Quality watches) =
200
9
=
10

3. Determine the number of quality watches produced each month using the
computed experimental probability.

Since the manufacturer has an average production of 10 000 watches each month,
9
and the experimental probability of having produced quality watches is 10 or 90%,

we can find the number of quality watches produced each month by multiplying
10,000 by 90%.

No. of quality watches = 10 000 × 0.9

= 9 000

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 Grade 8 • Unit 15: Probability

Therefore, the manufacturer could make about 𝟗 𝟎𝟎𝟎 quality watches each month
which is the best estimate.

Performance Assessment
This performance assessment serves as a formative assessment, divided into three sets
based on the student's level of learning. Click on the link provided on the lesson page to
access each worksheet.

● Worksheet I (for beginners)

● Worksheet II (for average learners)
● Worksheet III (for advanced learners)

Teacher’s Notes
For a standard performance assessment regardless of the student’s level of learning,
you may give the problem items provided in the Check Your Understanding section of
the study guide.

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 Grade 8 • Unit 15: Probability

Worksheet Answer Key

Worksheet I

1.
19
a. 86
21
b. 43
22
c. 43
37
d.
86
4
2. 7
4
3.
11
4
4.
9

5.
25
a. 59

b. experimental probability is greater than theoretical probability

c. experimental probability is greater than theoretical probability

Worksheet II

1.
49
a.
144
55
b. 144
53
c. 144
1
d. 2
14
2. 29

3. 22
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 Grade 8 • Unit 15: Probability
7
4. 13

5.
31
a.
112

b. experimental probability is greater than theoretical probability

c. experimental probability is less than theoretical probability

Worksheet III

1.
61
a. 106
141
b. 212
25
c. 106
37
d. 53

2. 545
3. 75
3
4. 8

5.
46
a. 217

b. experimental probability is greater than theoretical probability

c. experimental probability is less than theoretical probability

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 Grade 8 • Unit 15: Probability

Synthesis

Wrap-up To summarize the lesson, ask students the following questions:

1. What is the difference between experimental and
theoretical probability?
2. How did you compute the experimental probability of
simple events?

Application and To integrate values and build connection to the real world, ask
Values Integration students the following questions:
1. How does experimental probability help in making wise
predictions?
2. What are the other uses of experimental probability in real
life?

Bridge to the Next To spark interest for the next lesson, ask students the following
Topic questions:
1. As a student, how will you make wise decisions in the
future?
2. How can experimental and theoretical probability help you
in dealing with making life choices?

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 Grade 8 • Unit 15: Probability

Bibliography

Basic Mathematics. “Experimental Probability.” Retrieved 23 September 2019 from

http://bit.ly/31PukSr

Khan, Salman. “Finding Probability.” Khan Academy. Retrieved 23 September 2019 from
http://bit.ly/2TGtm7U

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