8 Dividing Fractions and Mixed numbers

Mathematics
Quarter 4 – Module 5

Illustrating an Experiment, Outcome,

Sample Space, and Event
 Dividing Fractions and Mixed numbers

Mathematics: Grade 8
Alternative Delivery Mode
Quarter 1 – Module 5: Illustrating an Experiment, Outcome, Sample Space, and Event
First Edition, 2020
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 illustrating an Experiment, Outcome,
Sample Space and Event

Most Essential Learning Competency:

Illustrates an Experiment, Outcome,
Sample Space, and Event

Most Essential Learning Competency:

Illustrate an experiment, outcome, sample space, and event. M8GE-IVf-1

In this lesson, the learner:

1. defines experiment, outcome, sample space, and events;
2. illustrates experiment, outcome, sample space, and events and;
3. demonstrates appreciation of illustrating experiment, outcome, sample space,
and events as an important skill needed to understand applications of
probability

This lesson helps the student to differentiate the concepts of an experiment,

outcome, sample space, and event from a given situation. Furthermore, the student will
appreciate the importance of these mathematical concepts which are used in our daily
lives in many different areas including insurance, science, marketing, government, and
many others.

Directions: Write the letter that you think is the best answer to each question on a
separate sheet of paper. Take note of all of the items that you were not able
to answer and look for the right answer as you go through this module.

1. What is a subset of a sample space called?

a. Cardinality b. Element c. Event d. Set
2. What term describes the manner of drawing cards, tossing a coin, or rolling a die
repeatedly?
a. Event b. Experiment c Outcome. d. Sample point
3. How many possible outcomes would there be if three coins were tossed at once?
a. 8 b. 6 c. 4 d. 2
4. What is the set of all possible outcomes of an experiment?
a. Events b. Outcome c. Sample space d. Venn diagram

Grade 8 Mathematics 3
 illustrating an Experiment, Outcome,
Sample Space and Event

5. In a restaurant, you have a dinner choice of one main dish, one vegetable, and one
drink. The choices for the main dish are pork and chicken meat. The vegetable choices
are broccoli and cabbage. The drink choices are juice and water. How many choices
are possible?
a. 8 b. 10 c. 12 d. 14
6. Arlene Joy got coins from her pocket which accidentally rolled on the floor. If there
were 8 possible outcomes, how many coins fell on the floor?
a. 3 b. 4 c. 8 d. 16
7. Nanette must pass through three doors as she walks from her company's foyer to her
office. Each of these doors may be locked or unlocked. List the outcomes of the
sample space.
a. {LLU, LUL, ULL, UUL, ULL, LUU}
b. {LLL, UUU}
c. {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
d. None of these.
8. A section of an exam contains two multiple-choice questions, each with three’ answer
choices (listed "A", "B", and "C"). List all the outcomes of the sample space.
a. {A, B, C}
b. {AB, AC, BA, BC, CA, CB}
c. {AA, AB, AC, BA, BB, BC, CA, CB, CC}
d. {AA, AB, AC, BB, BC, CC}

Use the situation to answer numbers 9 and 10.

Mr. Cruz, a grade 8 adviser, gave prizes to all of his students during their
Christmas party. To be fair, he made a spinner from a circular board and divided it into
4 congruent sectors. He wrote the following to each of the sectors: key chain, headset,
chocolate, a pack of candies. To determine their prize, each student is asked to spin the
spinner.

9. What is the experiment of the situation above?

a. giving the prizes c. claiming the prize
b. making the spinner d. spinning the spinner
10. Based on the situation, which of the following is not an outcome?
a. headset b. chocolate c. a pack of candies d. prizes

Your Perspective!
Direction: Study the following situations.

1. In a basketball game, how do the officials decide on what team will have the ball
position first? How about in a volleyball?
2. Have you ever played the snake and ladder game? How do you and your friends
decide on the number of moves you have to take for you to get to your next spot?
3. In playing games in a carnival, how high is your chance of winning in every
game you play?

Grade 8 Mathematics 4
 illustrating an Experiment, Outcome,
Sample Space and Event

Guide questions:
1. What is common among all the situations given?
2. Are there instances in your life wherein you are having a hard time deciding due
to some uncertainties of the consequences of your actions?
3. Is there a chance for us to know what our future will be?

Task 1
Directions: In this activity, please prepare any biased coin. Do the following
instructions and answer the questions that follow.
1. Toss the coin and note what side prevails.
2. Toss again the coin and take note of what side prevails.
3. Toss again the coin for the third time.

Questions:
1. Are results of flipping the coin three times the same? If not, what may be
the reason?
2. What do you call the activity, tossing the coin?
3. What do you call the result of the first, the second, or the third toss of the
coin?
4. What are the possible results upon tossing a coin?
5. Tossing a coin and getting a head is called ______?

Task 2
Directions: From the given situation, answer the questions that follow.

Getting an even number in rolling a die.

1. What is the sample space of the experiment?

2. What is the outcome of the experiment?
3. What are the events?

Tossing a fair coin obtains a fair result or unbiased outcome, that’s

why tossing the coin the second time may not be the same as the first
result. Yet, we cannot predict what happens next.
Task 1
Question 1- Are the results of tossing the coin three times the same? If not, what

Grade 8 Mathematics 5
 illustrating an Experiment, Outcome,
Sample Space and Event

may be the reason?

Answer: There is a chance of having the same results but not always
especially when using a fair coin.
A fair coin is an idealized randomizing device with two states (usually named
"heads" and "tails") which are equally likely to occur. It is based on the coin flip used
widely in sports and other situations where it is required to give two parties the same
chance of winning.

Question 2 - What do you call the action of flipping the coin?

Answer: Flipping of coin is called an experiment.

An experiment is any process or activity that generates a set of data wherein

each is influenced by chance.
 Example: Tossing a coin, rolling a die, spinning a spinner

Question 3- What do you call the result of the first, the second, or the third toss of the
coin?
Answer: The result of the first toss maybe head (H) or tail (T) and so with
the second and third is called outcome.
An outcome is the result of a single trial in an experiment.
Example: Tossing two coins and getting at least one head are { HH, HT,
TH}

Question 4 - What are the possible results upon tossing a coin?

Answer: The possible results of tossing a coin are Head (H) or Tail (T),
these are called sample space.
A sample Space is the set of all possible outcomes of the experiment.
Denoted as S= {H, T}. The element of sample space or each outcome is called
sample point.

Example: Picking an ace of a deck of cards, S= { }

Question 5- Tossing a coin and getting a head is called ______?

Answer: The activity of getting head is called an event.

An event consists of one or more outcomes and is a subset of the sample
space.
Example: Getting an even number from rolling a die

Task 2
Directions: From the given situation, answer the questions that follow.

Getting an even number in rolling a die.

Question 1- What is the sample space of the experiment?

Grade 8 Mathematics 6
 illustrating an Experiment, Outcome,
Sample Space and Event

Answer: The sample space is S={1,2,3,4,5,6}

Question 2- What are the outcomes of the experiment?

Answer: {2, 4, 6}

Question 3- What is the event of an experiment?

Answer: The event is getting an even number.

A. Independent Activity 1

Directions: From the given situation identify the following as experiment, outcome, sample
space, or event.

Rolling a die and tossing a coin at the same time, getting a number 2.
____________________ a. Rolling a die and tossing a coin.
____________________ b. Getting a number 2
____________________ c. S={1T, 2T, 3T, 4T, 5T, 6T, 1H, 2H, 3H, 4H, 5H, 6H}
____________________ d. {2T, 2H}

B. Independent Assessment 1
Directions: From the given situation identify the following as experiment, outcome,
sample space, or event.

Rotating a spinner wheel with five colors: yellow, blue, red, orange, green, and
getting primary color (blue, yellow, and red)

____________________ a. {red, yellow, blue}

____________________ b. S= {yellow, blue, red, orange, green}
____________________ c. Rotating a spinner wheel
____________________ d. Getting a primary color

C. Independent Activity 2

Directions: Based on the given situation below, identify the experiment, outcome, sample
space, or event.
1. Picking a card from a deck of cards and getting a heart.
Choose your answer from the box below

{2 to ace heart, 2 to ace diamond, 2 to ace club, 2 to ace spade}

Picking a card from a deck of cards
Getting a heart
{2 to ace heart}

Experiment-________________________________________
Outcome-__________________________________________
Sample space-______________________________________
Event- ____________________________________________

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 illustrating an Experiment, Outcome,
Sample Space and Event

D. Independent Assessment 2
Directions: Based on the given situation below, identify the experiment,
outcome, sample space, or event.

You ordered pizza from a certain food delivery raider. The choices are the
following:
for crust: thin and deep dish
for the topping: Hawaiian, pepperoni, and Gorgonzola and mushroom.

Experiment-________________________________________
Outcome-__________________________________________
Sample space-______________________________________
Event- ____________________________________________

Directions: Define experiment, outcome, sample space, and event based on

your understanding after answering all the activities and cite an
example in each.

Directions: Cite a situation you have experienced or encountered in real life and
identify the experiment, outcome, sample space, and event.

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 illustrating an Experiment, Outcome,
Sample Space and Event

Directions: Choose the letter of the correct answer and write your answers on a
separate sheet of paper.

1. The result of a single trial of an experiment is called ______.

a. Element b. Event c. Outcome d. Set
2. How many possible outcomes would there be if you tossed a coin and rolled a die
together?
a. 8 b. 12 c. 16 d. 20
3. In drawing cards and getting an ace, what term describes the manner of getting an
ace?
a. Sample point b. Outcome c. Experiment d. Event
4. What is the set of all possible outcomes of a probability experiment?
a. events b. sample space c. Venn diagram d. outcome
5. In a restaurant, you have a dinner choice of one main dish, one vegetable, and one
drink. The choices for the main dish are pork and chicken meat. The vegetable
choices are broccoli and cabbage. The drink choices are juice and water. If you
choose pork and any of the vegetables and drinks, how many choices are
possible?
a. 12 b. 10 c. 8 d. 4
6. Arlene Joy got two coins from her pocket which accidentally rolled on the floor. If
one of the coins ends up a head, what are the possible outcomes of the second
coin?
a. {HT, HH} b. {TH, TH} c. {HH, TT} d. {TT, TH, HT}
7. What are the possible outcomes in tossing three coins at the same time and
getting at least two tails?
a. {HTT, THT, TTH, TTT}
b. {HHH, HHT, HTH, HTT, THT, TTH, THH, TTT}
c. {HHH, TTT}
d. {HHH, HHT, HTH, THH}
8. In rolling two dice at the same time and getting the sum of 10, what is the event of
the experiment?
a. Rolling two dice c. a total of 36 sample spaces
b. Getting a sum of 10 d. a total of three outcomes

Use the situation to answer numbers 9 and 10.

Mr. Cruz, a grade 8 adviser, gave prizes to all of his students during their
Christmas party. To be fair, he made a spinner from a circular board and divided it into
4 congruent sectors. He wrote the following to each of the sectors: key chain, headset,
chocolate, a pack of candies. To determine their prize, each student is asked to spin the
spinner.
9. How many sample spaces are there?
a. 2 b. 4 c. 6 d. 8
Grade 8 Mathematics 9
 illustrating an Experiment, Outcome,
Sample Space and Event

10. Based on the situation, which of the following are/is an outcome?

a. headset b. chocolate c. a pack of candies d. All of these

Directions: From the situation below, determine the experiment, outcome,

sample space, and event.

Situation: A child is trying to get something from the top of their divider and
accidentally hits a small box with a die and made rolled to the floor. The die ends up to 5.

Experiment : __________________________________________________
Outcome : __________________________________________________
Sample : __________________________________________________
Event : __________________________________________________

Grade 8 Mathematics 10
 11 Grade 8 Mathematics
Additional Activities
Situation: A child will roll a die
Experiment: Rolling a die
Outcome: {1,2,3,4,5,6}
Sample Space: {1,2,3,4,5,6}
Event: Getting any number from 1 to 6
Assessment
1. C 6. A
2. B 7. A
3. D 8. B
4. B 9. B
5. D 10. D
Independent Assessment 2
Experiment: Ordering pizza from a delivery rider
Outcome: {thin & Hawaiian, thin & gorgozola and mushroom, thin & pepperoni}
Sample Space: { thin & Hawaiian, thin & gorgozola and mushroom, thin & pepperoni,
deep dish & Hawaiian, deep dish & gorgozola and mushroom, deep dish & pepperoni }
Event: ordering thin crust & any toppngs
Independent Activity 2
Experiment: Picking a card from a deck of cards
Outcome: {2 to ace heart}
Sample Space: {2 to ace Heart, 2 to ace diamond, 2
to ace club, 2 to ace spade}
Event: Getting a heart
Independent Assessment 1 Independent Activity 1 What I Know
1. Outcome 1. Experiment 1. C 6. A
2. Sample Space 2. event 2. B 7. C
3. Experiment 3. Sample space 3. A 8. C
4. Event 4. outcome 4. C 9. D
5. A 10. D
Sample Space and Event
illustrating an Experiment, Outcome,
 illustrating an Experiment, Outcome,
Sample Space and Event
REFERENCE:

Orines, F. B., Diaz, Z. B., Mojica, M. P., Manalo, C. B., Suzara, J. L., Mercado, J. P., Esparrago, M.
S., Reyes N. V. (2013). Next century Mathematics 8. Phoenix Publishing House, Inc., Quezon
City.
Abuzo, E., Bryant, M., Cabrella, J., Caldez, B., Callanta, M., Castro, A.,…, Ternida, C. (2013).
Mathematics- Grade 8 learners module: First edition. The Philippines.

Department of Education, Region VII, Division of Cebu Province

Email Address: cebu.province@deped.gov.ph

Grade 8 Mathematics 12