10
Mathematics
Learning Activity Sheet
Quarter 3 – MELC 8
Finding the Probability of (A U B)
Mathematics 10
Activity Sheet No. 8
First Edition, 2021
Published in the Philippines
By the Department of Education
Region 6 – Western Visayas
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Development Team of Mathematics 10 Activity Sheet
Writers: Janet J. Padernal
Ma. Enrequita G. Rivera
Editors: Jenny Anne L. Gange
Angeline Joy F. Jarangue
Ma. Elena E. Ecle
Illustrators: Janet J. Padernal
Ma. Enrequita G. Rivera
Layout Artist: Felizardo S. Valdez III
Schools Division Quality Assurance Team:
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Arthur J. Cotimo
Division of Guimaras Management Team:
Ma. Roselyn J. Palcat
Nordy D. Siason, Jr.
Elleda E. de la Cruz
Rosemarie D. Aclan
Arthur J. Cotimo
Felizardo S. Valdez III
Marve E. Gelera
Regional Management Team:
Ramir B. Uytico
Pedro T. Escobarte, Jr.
Elena P. Gonzaga
Donald T. Genine
Adonis A. Mosquera
ii
Introductory Message
Welcome to Mathematics 10!
The Mathematics Learning Activity Sheet is a product of the
collaborative efforts of the Schools Division of Guimaras and DepEd Regional
Office VI - Western Visayas through the Curriculum and Learning
Management Division (CLMD). This is developed to guide the learning
facilitators (teachers, parents, and responsible adults) in helping the learners
meet the standards set by the K to 12 Basic Education Curriculum.
The Learning Activity Sheet is self-directed instructional materials
aimed to guide the learners in accomplishing activities at their own pace and
time using the contextualized resources in the community. This will also
assist the learners in acquiring the lifelong learning skills, knowledge
and attitudes for productivity and employment.
For learning facilitator:
The Mathematics 10 Learning Activity Sheet will help you facilitate the
teaching-learning activities specified in each Most Essential Learning
Competency (MELC) with minimal or no face-to-face encounter between you
and learner. This will be made available to the learners with the
references/links to ease the independent learning.
For the learner:
The Mathematics 10 Learning Activity Sheet is developed to help you
continue learning even if you are not in school. This learning material
provides you with meaningful and engaging activities for independent
learning. Being an active learner, carefully read and understand the
instructions then perform the activities and answer the assessments. This
will be returned to your facilitator on the agreed schedule.
ii
Quarter 3, Week 8
Learning Activity Sheets (LAS) No. 8
Name of Learner:
Grade and Section:
School:
Date:
Finding the Probability of (A U B)
I.
Learning Competency with Code
Find the probability of (A U B) (M10SP-IIIg-h-1)
II.
Background Information for Learners
You have already learned how to illustrate the probability of union
of two events in your previous lesson. This time, you will find the
probability of (A U B) and able to apply it in solving real-life problems.
To find the probability of two events, remember these principles:
a. P(A U B) = P(A) + P(B) – P(A ∩ B), when two events have common
element/s
b. P(A U B) = P (A) + P (B), when two events have no common elements
c. P(A U B) = P (B), when set A is a subset of set B
Examples:
1. Among the 130 students of Remedios Vilches-SLNHS, 75 of them like
to eat at Remz Batchoy (R) while 65 of them like to eat at Nena’s
Eatery (N) and only 30 like to eat both at Remz Batchoy and Nena’s
Eatery. What is the probability that they like to eat either in Remz
Batchoy or in Nena’s Eatery?
Given:
Total number of students
Probability of students who eat at Remz batchoy
Probability of students who eat at Nena’s eatery
Probability of students who eat both at Remz batchoy
and Nena’s eatery
130
75
130
65
130
30
130
or 0.577
or 0.50
or 0.23
Solution:
P (𝑅 ∪ 𝑁) = P(R) + P(N) – P (R ∩ N)
75
130
=
=
110
130
65
130
+
or
–
30
130
11
13
Alternative Solution:
P(R 𝖴 N) = P(R) + P(N) – P (R ∩ N)
75
65
30
= 130 + 130 – 130
= 0.577 + 0.50 – 0.231
= 0.846
Therefore: P(R 𝖴 N) = P(R) + P(N) – P (R ∩ N) =
11
13
or 0.846
Venn diagram illustrates the probability of the union of R and N: P(R ∪ N)
R
0.346
N
0.231
0.269
0.154
R – Remz Batchoy; N – Nena’s Eatery
Note: The probability of choosing neither at Remz or Nena’s Eatery is
equal to 0.154 or
20
130
2. What is the probability of getting an odd or an even number when
a fair die is rolled?
O
E
Solution:
Sample Space = {1, 2, 3, 4, 5, 6}
P (E 𝖴 O) = P(E) + P(O)
=
=
3
6
3
+6
6
6
=1
3. What is the probability of getting a “6” or an even number when a fair
die is rolled?
Solution:
4
2
6
1
5
3
Sample Space = {1, 2, 3, 4, 5, 6}
P (E 𝖴 S) = P(E)
=
3
6
𝑜𝑟
= 0.5
1
2
Instructions: You may read and study the illustrative example on
pages 333 - 334 of Mathematics 10 Learner’s Module.
III.
Accompanying DepEd Textbook and
Educational Sites
Melvin M. Callanta, et.al., 2015. Mathematics 10 Learner’s
Module, First Edition, Rex Book Store, Inc., pages 332 – 334
IV. Activity Proper
Activity 1
Problem:
One hundred Grade 10 students from Remedios E. Vilches – San
Lorenzo National High School are interviewed if they are willing to join
either in volleyball (V), in basketball (B) and in both upcoming
sportsfest. Below is the result of the survey.
Sport
Volleyball
Basketball
Both Volleyball and
Basketball
Number of
students
55
75
35
Answer the following:
a. What is the probability of the students who are willing to join
volleyball?
b. What is the probability of the students who are willing to join
basketball?
c. What is the probability of the students who are willing to join
either in volleyball or in basketball?
Activity 2:
To summarize what you have learned in this lesson, answer the
following questions:
a. How do you find the probability of the two events if:
• they have common element/s?
V.
•
they have no common element/s?
•
event A is a subset of event B?
Reflection
In this lesson, I learned that
VI.
Answer Key