MATH 6 Q4 Module 8
MATH 6 Q4 Module 8
MATH 6 Q4 Module 8
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This Self-Learning Module (SLM) is prepared so that you, 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 Teachers are also
provided to our facilitators and parents for strategies and reminders on how they
can best help you on your home-based learning.
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this SLM. Use a separate sheet of paper in answering the exercise and tests.
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.
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What I Need to Know
This module provides varied activities that will help you learn about
making predictions of events based on the results of experiments.
What I Know
Directions: Choose the correct answer by writing the letter of your choice in your answer
sheet.
1. It is any activity with an observable result that can be done repeatedly and involves
chances.
a. experiment c. probability
b. outcome d. sample space
5. These are events in which the occurrence of the first event affects the occurrence of the
second event.
a. Dependent events c. Independent events
b. Experimental Probability d. Theoretical Probability
6. Ellen has a bag with 2 blue marbles and 3 red marbles in it. She is going to randomly pick
the marbles from the bag, find the theoretical probability of getting a blue marble.
a. c.
b. d.
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7. John is going to roll a 6-sided die 24 times. What is the best prediction for the number of
times that John will have the number 5?
a. Exactly 4 times
b. Close to 4 times but probably not exactly 4 times
c. Exactly 6 times
d. Close to 6 times but probably not exactly 6 times
8. Ellen is going to spin the spinner 5 times. The spinner is divided into equal sections. What
is the best prediction that the spinner will land in the shaded region?
a. Exactly 4 times after 5 spins
b. Close to 4 times but probably not exactly 4 times
c. Exactly 5 times after 5 spins
d. Close to 5 times but probably not exactly 5 times
9. There are 4 marbles in a bag. 3 marbles are blue, and 1 is red. What is the probability that
a red marble will be picked?
a. c.
b. d.
10. What is/are the chance/s of rolling a "4" with a die (singular for dice)?
a. c.
b. d.
What’s In
Directions: Answer the following questions. Write your answers on a separate answer sheet.
____________________________________
2. Look at the menu below. How many ways can you order snacks?
Kakanin Beverages
Putong Puti Tea
Biko Juice
Kutsinta
____________________________________
3. When a die is rolled, how many outcomes are possible?
____________________________________
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4. Complete the diagram to find all the possible ways the two coins can land.
5. Make a list of outcomes when two coins are tossed at the same time.
____________________________________
What’s New
What is It
Example 1: When a coin is tossed, there are two possible outcomes: heads (H) or
tails (T).
In this example, tossing a coin is the experiment and the outcomes are heads or
tails.
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Example 2: When a single die is thrown, there are six possible outcomes: 1, 2, 3, 4, 5, 6.
In this example, throwing a die is the experiment and the outcomes are 1, 2, 3, 4, 5,
6.
Example 3: If a coin is tossed 10 times, find the theoretical probability of getting a head.
Solution: In a coin there is only one face with a head and there are two possible outcomes,
the head and the tail. Each face is equally likely to occur, so:
Theoretical probability (E) = Number of favorable outcomes =
Number of possible outcomes
Note: E refers to event.
Example 4: If a coin is tossed 10 times, and the head appears 6 times, find the experimental
activity of getting a head.
Solution 1: In this problem, the head appears 6 times, it is the number of times favorable
outcomes occur and the number of trials is 10.
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Example 5: A drawer contains 7 white socks and 5 black socks. Two socks are drawn at
random, one after the other, without replacement. Find the probability of drawing
two white socks in a row.
First Draw:
Number of white socks
P (white) = = The first sock is not replaced.
Total Number of socks
Second Draw:
There are now 6 white
P (white) = Number of white socks minus 1 = socks that can be
Total Number of socks minus 1
drawn out of 11 socks.
This is called dependent events, events in which the occurrence of the first event
affects the occurrence of the other events. On the other hand, independent events are
events in which the occurrence of the first event does not affect the occurrence of the other
events.
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What’s More
Independent Activity 1
Directions: Find the probability of the spinner at the right stopping on each of the following.
Write your answers on a separate answer sheet.
1. A four
2. An odd number
3. An even number
4. A number less than 5
5. A number less than 8
Independent Assessment 1
Directions: Read and solve the given experiment. Write your answers on a separate answer
sheet.
Pupils were surveyed about the number of books inside their bags. The table shows
the results. Write each experimental probability as fraction in simplest form.
Independent Activity 2
Directions: Solve the following. Write your answer on a separate answer sheet in fraction
form and in simplest form if necessary.
1. A bag contains 40 marbles, 28 red ones and 12 blue ones. A marble is picked at random
from the bag. What is the probability of picking:
a) a red marble. __________
b) a blue marble. __________
c) a yellow marble. __________
2. In a class of 45 students, 15 are in the Math Club and 10 are in the Art Club. If a student
is selected at random, what is the probability that the selected student is:
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Independent Assessment 2
Directions: Find the theoretical and experimental probability. Write your answers on a
separate answer sheet.
Carlo picks a card at random from a box containing 6 cards with the letter “M”, 4
cards with the letter “A”, 5 cards with the letter “T”, and 2 cards with the letter “H”. After he
picks a card, he records the result and places it back inside the box. He repeats this 30
times. Shown below is the result of the experiment.
Outcome M A T H
Number of times obtained 12 6 10 2
Independent Activity 3
Directions: Read and solve the following.Write your answers on a separate answer sheet.
1. A two-digit number is written at random. Determine the probability that the number will be:
a) an odd number __________
b) an even number __________
c) larger than 75 __________
Independent Assessment 3
Directions: Answer the following.Write your answers on a separate answer sheet.
1. If a coin is tossed 8 times, predict the number of times you would expect to get a head.
__________
2. A spinner has 4 equal sectors numbered 1 to 4. If you spin it, what is the probability of
landing on a number less than 4?
__________
3. Inside a box are 5 blue, 7 red, 6 yellow and 2 green balls. If a ball is picked at random
from the box, what is the probability of picking:
a) a blue ball __________
b) a green ball __________
c) a brown ball __________
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What I Have Learned
When we use a formula to find a probability of an event, we are finding the theoretical
probability. It is what we are expecting to happen.
Independent events are events in which the occurrence of the first event does not
affect the occurrence of the other events.
What I Can Do
Directions: Read and solve. Write your answer on a separate answer sheet.
A drawer contains 2 black socks, 4 white socks and 4 gray socks. Two socks
are drawn at random, one after the other, without replacement. Complete the equation
to find each probability.
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Assessment
Directions: Choose the letter of the correct answer and write it in your answer sheet.
1. A letter is selected at random from the word “MAKATAO.” How many outcomes are
there in the sample space?
a. 5 c. 7
b. 6 d. 8
2. In the word “MATH,” how many outcomes are there in the event that the letter
selected is a consonant.
a. 1 c. 3
b. 2 d. 4
3. A die is rolled. What is the probability of a 2 turning up?
a. c.
b. d.
4. If two dice are rolled, find the probability of getting the sum of 9.
a. c.
t
b. d.
5. A spinner has 5 equal sectors colored blue, red, yellow, green and white. What is the
probability of landing on yellow?
a. c.
b. d.
6. Numbers from 1 to 20 are placed inside a jar and a number is drawn at random. Find the
probability of drawing an even number.
a. 1 c.
b. d.
7. A pupil is selected at random from a class of 18 boys and 12 girls. What is the probability
that the pupil chosen is a girl?
a. c.
b. d.
8. If a coin is tossed 70 times, predict the number of times you would expect to get a tail.
a. 70 c. 35
b. 50 d. 15
9. There are five coins in your pocket. One is a 25-centavo coin, a 5-peso coin and the rest
are all 1-peso coins. What is the probability of randomly picking a 5-peso coin?
a. c.
b. d.
10. Find the probability of getting a sum of 14 when a pair of dice is thrown.
a. 0 c.
b. d. 1
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Additional Activities
Directions: Perform the experimental probability of rolling a pair of dice.
1. Complete the table by listing all the possible outcomes in the sample space.
Die 1
1 2 3 4 5 6
Die 2
1 (1, 1)
3. Roll the dice 10 times, list how many times you would get a sum of 10.
______________________________________________________________________
4. If you will roll the dice 30 times, can you predict how many times you would expect to get
a sum of 6. __________
5. Now, roll the dice 30 times and list the outcomes that will give a sum of 6. Compare the
result of your Experimental probability to the result of theoretical probability in number 4.
Do they have the same result? Why? Why not?
_____________________________________________________________________
_____________________________________________________________________
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What I Know Independent Assessment 2
Theoretical Prob. Experimental Prob.
1. a 6. b 1
2. c 7. b 2. 0 0
3. d 8. b 3.
4. d 9. a 4.
5. a 10. a 5.
What’s In Independent Activity 3
1. 1, 2, 3, 4, 5, 6, 7, 8 1. 2.
2. 6 ways a) c) a)
3. 6 outcomes b) b)
4.
5. (H, T), (T, H), (H, H), (T, T)
What’s New
25 times
What’s More What I Can Do
Independent Activity 1 a) First draw: P (black) =
1. Second draw P (black) =
2. P(black, then black) =
t
3. b.) First draw: P(white) =
4. Second draw: P (gray) =
5. P(white, then gray) =
t
Independent Assessment 1
t
A. Assessment
1. 1. a
2. 2. c
3. 3. a
B. 4. a
4. 48 5. d
5. 36 6. b
Independent Activity 2 7. c
1. 8. c
a) 9. d
b) 10. a
㌳
c) 0
㌳
2.
a)
b)
Answer Key
References
A. Books
Perez, Marjoseph H. et. al... “21st Century Mathletes 6” Textbook. 1253 Araneta
Avenue, Quezon City: Vibal Group Inc. 2016
B. Electronic Sources
LRMDS Portal. “DLP Gr. 6 Module 67: Making simple predictions.” DepEd
https://lrmds.deped.gov.ph/detail/7324
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