This is the Grade 5 Mathematics Quarter 4 Module 16 self-learning module, “Performing Experimental Probability and Records Results by Listing.” It is for Grade 5 learners studying at home or in class, and for the parents and teachers who guide them. After working through it, learners should be able to carry out a simple probability experiment, list all the possible outcomes, and write a probability as a fraction, decimal, or percent.
The module was written by Violeta T. Saldaña and published as a first edition in 2020 by the Department of Education, Region VIII, under the Alternative Delivery Mode.
What learners will learn
By the end of the module, learners are expected to:
- perform experimental probability and record results by listing
- appreciate the importance of performing experimental probability and recording results by listing
The module says learners should already know how to reduce fractions to lowest terms, change decimals to percents and back, and describe experimental probability.
Key ideas: probability and favorable outcomes
Probability is the mathematics of chance. It tells how likely or unlikely something is to happen. Its value goes from 0 to 1:
- 0 means the event is impossible.
- 1 means the event is certain.
- 1/2 means the event is equally likely to happen or not.
A probability can be written as a fraction, a decimal, or a percent.
Experimental probability is found from the results of an experiment, that is, from what actually happens when you try it out. It is the ratio between the number of times the event occurs and the total number of trials. When the result is the one you expected, it is called a favorable outcome.
The module uses this formula:
P = favorable outcomes / total possible outcomes
Examples from the module
- The party prize: There are 20 guests, and Alfred wins only if his card is drawn. His chance is 1/20 = 0.05 = 5%.
- The letter cube: A cube has the letters S, E, N, S, E, S on its faces. Tossing it once gives 6 possible outcomes. The probability of tossing an S is 3/6, an E is 2/6, and an N is 1/6.
- The coin toss: A coin is tossed 60 times and lands on heads 27 times. The experimental probability of heads is 27/60, which reduces to 9/20.
Key ideas: listing outcomes and tree diagrams
To find a probability, you first need to know everything that can happen. A sample space is a list of all the possible outcomes of an activity or experiment.
- Spinner example: A spinner has 8 regions numbered 1 to 8. Its sample space is all eight numbers, 1 through 8.
- Snack menu example: A menu has 3 burgers (regular, cheeseburger, pizza burger) and 2 drinks (juice, tea). Using letters, the list of choices is R-J, R-T, C-J, C-T, P-J, and P-T, so there are 6 ways to order.
A tree diagram shows the same combinations as branches. Each of the 3 burgers branches into 2 drinks, so 3 x 2 = 6 ways to order a snack.
Activities in the module
| Part | What learners do |
|---|---|
| What I Know | A 10-item multiple-choice pretest on finding chances, written as fractions |
| What’s In | Review: label events as 0 (impossible), 1/2 (equally likely), or 1 (certain) |
| What’s New and What Is It | The party example, the formula, and listing and tree diagrams |
| Activity 1: Pick a Color | Draw marbles (3 green, 2 blue, 1 red) from a box 20 times, putting each back, and record results in a tally table |
| Activity 2 | Find chances about days of the week, a coin, marbles, and a die |
| Activity 3 | Read a table of card results (blue 27, green 15, red 8) and find the trials and probabilities |
| What I Have Learned | Fill in the blanks on key terms |
| What I Can Do | Find the probability of drawing each letter of the name LORRAINE from a box |
| Assessment | A 10-item multiple-choice posttest |
| Additional Activities | Find the probability of a picture spinner landing on each symbol |
How to use this module
Start with the pretest (What I Know) to see what you already know, then go through each part in order. Write your answers on a separate sheet of paper or in your notebook, and do not mark the module. Finish with the Assessment to check your learning. Answer keys for every part are on the last pages; the module asks learners to use them honestly, only after answering.
- Learners: For Activity 1, you need a box and 6 marbles (or any small objects in three colors). Put the marble back after each draw.
- Parents: Help gather the materials for the experiment and remind your child to try each task before checking the answer key.
- Teachers: Activity 1 answers will vary because they come from each learner’s own trials. Please check a few answer key items before using them. For example, the probability that a coin shows neither head nor tail should be 0 (impossible), which matches the module’s own explanation of 0.
If learners have questions or trouble with any task, the module encourages them to ask their teacher or facilitator.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 5 Mathematics, Quarter 4. It is Module 16, titled Performing Experimental Probability and Records Results by Listing.
What is experimental probability?
It is a probability found from the results of an actual experiment. It is the ratio between the number of times an event happens and the total number of trials, such as 27 heads out of 60 coin tosses, or 9/20.
What is a sample space?
A sample space is a list of all the possible outcomes of an activity or experiment. For a spinner with regions numbered 1 to 8, the sample space is the numbers 1 to 8.
Does the module have an answer key?
Yes. Answer keys for the pretest, activities, and assessment are on the last pages of the module. A few items are worth checking before use.
What materials does the hands-on activity need?
Activity 1, Pick a Color, needs a box and 6 marbles: 3 green, 2 blue, and 1 red. Learners draw a marble 20 times, put it back each time, and record the colors.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 4 – Module 16: Performing an Experimental Probability and Records Result by Listing
[illustration: teacher and learners studying outdoors and at a table, with a globe and a lamp]
CO_Q4_Mathematics5_ Module16
Mathematics – Grade 5 Alternative Delivery Mode Quarter 4 – Module 16: Performing Experimental Probability and Records Results by Listing First Edition, 2020
Republic Act 8293, Section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for the exploitation of such work for a profit. Such agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this book are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Development Team of the Module
| Role | Name(s) |
|---|---|
| Writer: | Violeta T. Saldaña |
| Editor: | Niaan L. Atis, Jaysam M. Casaljay, Elizabeth Deligero |
| Reviewers: | Renato S. Cagomoc, Joshua Sherwin T. Lim, Rolando M. Lacbo, Irene G. Dimakiling, Geraldine P. Sumbise |
| Illustrator: | Jaime E. Sagayap Jr. |
| Layout Artist: | Noel E. Sagayap, Razle L. Jabelo, Cherry Lou O. Calison |
| Management Team: | Ramir B. Uytico, Arnulfo R. Balane, Rosemarie M. Guino, Joy B. Bihag, Ryan R. Tiu, Sarah S. Cabaluna, Thelma Cabadsan-Quitalig, Elena S. De Luna, Renato S. Cagomoc, Noel E. Sagayap, Geraldine P. Sumbise, Joshua Sherwin T. Lim |
Printed in the Philippines by Department of Education – Region VIII
Office Address : DepEd Regional Office No. 8, Candahug, Palo, Leyte Telefax : (053)-323- 3156 E-mail Address : region8@deped.gpv.ph
Mathematics Quarter 4 – Module 16: Performing Experimental Probability and Records Results by Listing
5
Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate sheet of paper in answering the exercises and tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
[illustration: target with an arrow]
Good day Mathletes! This module was designed and written to help you gain understanding and test your ability in Performing Experimental Probability and Records Results by Listing!
We knew that an experimental probability is the ratio between the number of times the event occurs and the total number of trials. It is determined by doing an experiment. When dealing with probabilities, it is important to be able to identify all the possible outcomes. In real life, whenever we do an experiment, two things can happen, either the one we expect or the one that we do not. When the result is what we expected, then it is the favorable outcome.
So, what are you waiting for? Stay focused and start-up.
At the end of this module, you are expected to:
- perform experimental probability and record results by listing
- appreciate the importance of performing experimental probability and records results by listing
Before going any further, let us check your understanding about performing experimental probability and records results by listing.
What I Know
[illustration: pencil]
Directions: Read carefully each statement below. Express the outcomes of your prediction in fraction. Choose the letter that corresponds to the best answer. Write the chosen letter on a separate sheet of paper.
What is the chance that you will get a passing score in your 10-item Math quiz?
- (A) 3
- (B) 4
- (C) 5
- (D) 2
What is the probability that a newly born puppy is a girl?
- (A) 1
- (B) 2/2
- (C) 1/2
- (D) 1/4
1 CO_Q4_Mathematics5_ Module16
There are 6 marbles in a bag. One is red; 2 – yellow; and 3 – green. What is the chance of picking yellow marble?
- (A) 1/6
- (B) 3/6
- (C) 5/6
- (D) 2/6
What is the chance of picking red? Please refer to question number 3.
- (A) 2/6
- (B) 3/6
- (C) 5/2
- (D) 1/6
What is the chance of picking green?
- (A) 3/6
- (B) 2/6
- (C) 1
- (D) 1/6
Van has 5 white socks, 4 blue socks and 6 black socks in a drawer. If he pulls one out without looking, what is the probability that he will pull out of black socks?
- (A) 6/15
- (B) 5/15
- (C) 4/15
- (D) 10
A die is marked with the first 6 letters of the alphabet rather than numbers. What are the chances that when the die is rolled a vowel will show up?
- (A) 1/6
- (B) 3/6
- (C) 1/35
- (D) 4
What is the probability that a 5 or 6 will be showing on top after the number cube is tossed?
- (A) 5/6
- (B) 1/6
- (C) 1/3
- (D) 6
A bag of candies contains 10 red, 12 blue, 8 green, 6 brown, and 14 yellow candies. If Robert removes one candy from the bag at random what is the probability that it will be blue?
- (A) 10/50
- (B) 6/50
- (C) 8/50
- (D) 12/50
A spinner numbered 1-8 is spun. What is the probability of spinning a factor of 18?
- (A) 4
- (B) 2
- (C) 3
- (D) 1
2 CO_Q4_Mathematics5_ Module16
Lesson 1: Performing Experimental Probability and Records Results by Listing
In order to perform experimental probability and records results by listing, you need to master the skills on reducing fraction to lowest term, changing decimal to percent and vice versa and describe experimental probability. Because these will help you gain understanding the concept of the lesson. In this module, you will learn how to perform experimental probability and records results by listing. Are you ready?
What’s In
[illustration: puzzle pieces]
In the previous lessons, you were able to learn the concept of describing experimental probability.
Also, you learned how to perform experimental probability. Note that, by doing a probability experiment, we can determine the number of times an event occur. We use a table and record the outcome of probability experiment. The probability can be approximated as the fraction of the number of times an event occurs by the number of times the experiment was performed.
Note that, a probability is the mathematics of chance. Probability is used to describe how likely or unlikely it is that something will happen. Probability may be given in fraction, decimal, or percent. The value of probability ranges from 0-1 (0 means the event is impossible to happen, while 1 means the event is certain to happen).
Let us refresh your memory and try to answer the following exercises:
Directions: Write 0 for impossible to happen, 1/2 for equally like to happen and 1 for certain to happen.
- A frog will swim in the water.
- You will finish reading this sentence.
- The teacher teaches the pupils.
- The probability of getting a number more than 6 in tossing a die is 1/6.
- The cat drives the car.
3 CO_Q4_Mathematics5_ Module16
What’s New
[illustration: seedling]
From the previous lesson, you were taught on how to describe experimental probability. In this lesson, we will deal with performing experimental probability and records results by listing.
Do you know that a probability can be expressed into fraction, decimal or percent form? You will understand this concept as you go along with this module.
Let us study this example:
There are 20 guests in the party, and each have an equal chance to win the prize. Alfred wins only if his card is drawn. What is his chance of winning the prize?
[illustration: a student walking toward a crowd of party guests]
What Is It
[illustration: magnifying glass with question mark]
Experimental probability is a probability determined from the results of an experiment and also experimental probability is what actually happens when we try it out.
In real life, whenever we do an experiment, two things can happen, either the one that we expect or the one that we do not. When the result is what we expected, then it is a favorable outcome.
4 CO_Q4_Mathematics5_ Module16
An experimental probability is the ratio between the number of times the event occurs and the total number of trials.
$$P = \frac{\text{favorable outcomes}}{\text{total possible outcomes}}$$
So, the answer to the presented problem above is:
$$\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}} = \frac{1}{20} = 0.05 = 5%$$
Therefore, Alfred has $\frac{1}{20}$ or 5% chance to win the prize.
When dealing with probabilities, it is important to identify all the possible outcomes. The following are some of the methods that we can use:
When a cube with letters S, E, N, S, E, and S on its faces is tossed once, there are 6 total outcomes and the possible outcomes of tossing an S, E, and N. We could also say that the probability of tossing each letter is
Probability of tossing an $S = \frac{3 \rightarrow \text{favorable outcomes } {S,S,S}}{6 \rightarrow \text{total possible outcomes } {S,E,N,S.E.S}}$
Probability of tossing an $E = \frac{2 \rightarrow \text{favorable outcomes } {E,E}}{6 \rightarrow \text{total possible outcomes } {S,E,N.S,E,S}}$
Probability of tossing an $N = \frac{1 \rightarrow \text{favorable outcome } {N}}{6 \rightarrow \text{total possible outcomes } {S,E,N,S,E,S}}$
Listing and Tree Diagrams
To calculate probability, we need to know all the different things that can happen. A sample space is a list of all the possible outcomes of an activity or experiments.
Example 1: Suppose you spin the spinner. Make a sample space for the spin.
[illustration: circular spinner divided into 8 regions numbered 1 to 8, with an arrow pointing to the region numbered 6]
Solution: The spinner can land on 8 different regions. To make the sample space, list all the possible outcomes of the spin.
Answer: The sample space is: 3, 4, 5, 6, 7, 8, 1, 2
Example 2: Look at the menu below. How many ways can you order snacks?
HAMBUGERS Regular Burger Cheeseburger Pizza burger BEVERAGES Juice Tea
There is more than one way to solve this problem.
Solutions:
LISTING: Use R for regular, C for cheese, P for pizza, J for juice and T for tea.
Outcomes:
a. R, J b. R, Tc. C, J b. d. C, T e. P, J f. P, T
The list shows there are 6 ways to order snacks.
TREE DIAGRAM
[chart: tree diagram; TREE DIAGRAM (untitled)]
- Snack → Regular → Juice → Regular burger and juice
- Snack → Regular → Tea → Regular burger and tea
- Snack → Cheeseburger → Juice → Cheeseburger and juice
- Snack → Cheeseburger → Tea → Cheeseburger and tea
- Snack → Pizza Burger → Juice → Pizza burger and juice
- Snack → Pizza Burger → Tea → Pizza burger and tea
In the diagram, we can see that for each of the three kinds of hamburgers, there are two beverage choices. Thus, 3×2=6, there are six ways to order snacks.
What’s More
Activity 1
PICK A COLOR
Materials: a box, 6 marbles, (3 green, 2 blue, 1 red)
Procedure:
a. Put the marbles in the box. Without looking, draw one marble from the box and record the color in the table below. b. Put the marble back in the box. Do more 19 trials. Replace the marble each time after recording the color. c. How many times out of 20 did you draw a blue marble? Green marble? And red marble?
| color | tally | number |
|---|---|---|
| Green | ||
| Blue | ||
| Red |
Answer the following questions:
- Did you enjoy performing the activity?
- Did you follow the procedure in performing the probability experiment?
- How did you express the outcomes of your probability experiment?
- What did you notice from the results of your probability experiment?
Activity 2
Directions: Express the outcomes of your prediction. Write your answer in your notebook.
- Consider the days of the week. What is the chance that you choose a day which begins with letter T? What is the chance that the day you choose has less than 15 letters?
- Toss a coin. What is the probability that neither the head nor the tail shows up?
- A bag contains 10 marbles – 8 yellow marbles, and 2 black marbles. Rona took a marble and returned it. After 10 trials, a yellow marble was picked 6 times. Find the experimental probability of getting red marble.
- If you roll a die, what is the probability that you will get even numbers?
Activity 3
The table shows the results of a card experiment. Each time a card was picked, it was returned to the bag.
| Card Experiment | |
|---|---|
| Outcome | Number |
| blue | 27 |
| green | 15 |
| red | 8 |
- How many trials of picking a card were made?
- How many times was the blue card picked?
- What is the experimental probability of picking a red card?
- If 10 blue cards were in the bag, how many green cards would you predict?
What I Have Learned
By doing probability experiment, we can determine the number of times an event occur. We use a table and record the outcome of the probability experiment.
A. Fill in the blanks.
(1) _____________ is a probability determined from the results of an experiment and also experimental probability is what actually happens when we try it out. When we do something and we are expecting a result by (2) _____________ or we are not certain of what the result will be, in probability, we call it an (3) _____________. The uncertain result is called an (4) _____________.
In real life, whenever we do an experiment, two things can happen, either the one that we expect or the one that we do not. When the result is what we expected, then it is the favorable outcome.
An experimental probability is the (5) _____________ between the number of times the event occurs and the total number of trials.
What I Can Do
In real life, whenever we do an experiment, two things can happen, either the one that we expect or the one that we do not. When the result is what we expected, then it is the favorable outcome.
An experimental probability is the ratio between the number of times the event occurs and the total number of trials.
Directions: Read the given situation and describe the experimental probability. The first one is done for you.
Example: A coin is tossed 60 times. A head appeared twenty-seven times. Find the experimental probability of getting heads.
Solution: $\frac{\text{number of times the event occurs (heads appeared)}}{\text{total number of trials}} = \frac{27}{60} = \frac{9}{20}$
Therefore, the experimental probability of getting heads is $\frac{9}{20}$
Directions: Read the given situation and record the probability.
Lorraine puts cards with letters of her name into a box. What is the probability that the card she pulls out is /are_________?
[illustration: eight empty boxes in a row, for letter cards]
a. L? _________ b. O? _________ c. R? _________ d. A? _________ e. I? _________ f. N? _________ g. E? _________
Assessment
Directions: Read carefully each statement below. Choose the letter that corresponds to the best answer. Write the chosen letter on a separate sheet of paper.
- Toss a die, what is the probability that you will get 4 on top?
- (A) 1/6
- (B) 1/8
- (C) 2/6
- (D) 3/6
- What is the probability that you can choose a rose from a flower shop selling sunflower, tulips, dahlia?
- (A) 1/2
- (B) 0
- (C) 1
- (D) 2
- Toss a coin. What is the probability that neither the head nor the tail shows up?
- (A) 2/1
- (B) 1/3
- (C) 1/2
- (D) 2/2
- What if there are 3 white ribbons, 4 pink ribbons and 5 red ribbons in your box. What is the chance of choosing a red ribbon?
- (A) 5/12
- (B) 3/12
- (C) 4/12
- (D) 1/12
- What is the chance of choosing a ribbon that is not red?
- (A) 12/12
- (B) 5/12
- (C) 3/12
- (D) 7/12
- If you choose a day at random, what is the probability of choosing Monday?
- (A) 2/7
- (B) 1/7
- (C) 3/7
- (D) 7/7
- What is the probability of choosing a day with only 3 letters?
- (A) 1/7
- (B) 2/7
- (C) 3/7
- (D) 0/7
- In tossing a coin there are two possible outcomes.
- (A) yes
- (B) no
- (C) maybe
- (D) yes/no
- When the result is what we expected, then it is the favorable outcome.
- (A) no
- (B) maybe
- (C) yes
- (D) yes/no
- Combination of outcomes can be shown on a tree diagram.
- (A) no
- (B) yes
- (C) maybe
- (D) yes/no
Additional Activities
You made it! Finally, you’re on the last activity. Answer it all correctly so you could climb at the top and get your trophy.
Directions: What is the probability that this spinner will land on _____? Write in fraction form.
- [illustration: star]
- [illustration: heart]
- [illustration: crescent moon]
- [illustration: cloud]
- [illustration: lightning bolt]
[illustration: circular spinner divided into 8 regions, containing clouds, stars, hearts, and crescent moons]
Answer Key
[transcriber’s note: this page is printed upside down; the answer key is transcribed in reading order]
What I Know
- A
- C
- D
- D
- A
- A
- C
- C
- D
- D
What I can do
- L (1/8)
- O (1/8)
- R (2/8)
- A (1/8)
- I (1/8)
- N (1/8)
- E (1/8)
What’s In
- 1
- 1
- 1
- 0
- 0
What I Have Learned
- Experimental probability
- chance
- experiment
- outcome
- ratio
What’s More
Activity 1
1-5. Answer may vary
Activity 2
- 2/7, 1
- ½
- 0
- 3/6 or ½
Activity 3
- 50
- 27 times
- 4/25
- Answer may vary
Assessment
- A
- B
- C
- A
- D
- B
- D
- A
- C
- B
Additional Activities
- 2/8 or 1/4
- 3/8
- 1/8
- 2/8 or 1/4
- 0/8
References
Borromeo, Melody G. 2016. Teacher’s Manual 5. 21st Century MATHletes. Vibal Group,Inc.
Lumbre, Angelina P., and Alvin C. Ursua. 2016. 21St Century MATHletes 5 Textbook. Quezon City: Vibal Group, Inc.
Perez, Marjoseph H.,and Donnel P. Placer,Jaime R. Burgos, 2016. 21st Century MATHletes 6 Textbook. Quezon City: Vibal Group, Inc.
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Telefax: (632) 8634-1072; 8634-1054; 8631-4985
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