Lesson Exemplar on Math Grade 10 involving Mutually Exclusive and Not Mutually Exclusive Events for the Third Quarter

1. LESSON
EXEMPLAR
School
Jacobo Z. Gonzales Memorial National
High School Grade Level 10
Teacher KAYCEE D. BALABAG Learning Area Mathematics
Teaching Date Quarter Third
Teaching Time No. of Days 1
I. OBJECTIVES At the end of the lesson, the students are expected to:
a. Determine mutually exclusive and not mutually exclusive events;
b. Solve the probability of a mutually exclusive and not mutually exclusive
events.
c. Appreciate the usage of mutually exclusive and not mutually exclusive
events in real life situations.
(According to Zhou (2017), Learning objectives should be used to direct students as they complete the
course and to gauge their level of understanding. Excellent learning objectives provide students a
direction when reviewing the content and getting ready for the assessment. The most effective learning
objectives are those that can be measured and put into practice.)
A. Content Standards Identifying mutually exclusive events and solving problems involving probability
B. Performance Standards The learner is able to use precise technique and probability in formulating
conclusions and in making decisions.
C. Most Essential Learning
Competencies (MELC)
The learner illustrates mutually exclusive events (M10SP-IIIi-1)
E. Enabling Competencies
(If available, write the attached
enabling competencies)
II. CONTENT Mutually Exclusive and Not Mutually Exclusive Events
III. LEARNING RESOURCES
A. References
a. Teacher’s Guide Pages
b. Learner’s Material Pages Math Leaner’s Package
Growing Up with Math
c. Textbook Pages
d. Additional Materials from
Learning Resources
CO_Q3_Mathematics 10_Module 30
Vygotsky's Zone of Proximal Development and Scaffolding - Educational Technology
B. List of Learning Resources for
Development and Engagement
Activities
Pictures and Visuals through Microsoft PowerPoint
Quizziz.com
Google Classroom for distribution of materials, activities etc.
IV. PROCEDURES
A. Introduction **The content of the lesson will be presented.
**Learning objectives will be presented to guide the learners in their learning targets.
LEARNING TASK 1: Preliminary Activity
The Venn diagram at the right shows the probability of Grade 10 students playing
either Mobile Legend (ML) or Clash of Clans (CoC). Use the Venn diagram to find
the probabilities of
1. P(ML)
2. P(CoC)
3. P(ML U CoC)
4. P(ML ∩ CoC)
5. P(ML U CoC)’

2. B. Development (The teacher used Vygotsky’s concept of scaffolding. It used when the teacher begins by showing
students how new information can be used. Then the teacher guides the students as they use the new
information. Then the teacher has students use the new information independently. The concept of
mutually exclusive and not mutually exclusive events is sometimes confusing to students. Students could
first be given a pair of different events and asked if the two events could happen at the same time. For
example Event A: tossing a coin and getting heads and Event B: tossing a coin and getting tails.)
LEARNING TASK 2: It can be or cannot?
Tell whether if the given situations can happen at the same time or not. (Quizziz.com)
1. Throwing the ball up and down
2. Raising your arm and bending
your knees
3. Running and sweating
4. Determining the sex of offspring in a
genetic cross
5. Weight loss and gain weight following
treatment with a drug
** With the attack of Covid-19 pandemic, what do you think made the IATF to
declare ECQ in one province and GCQ in the other? Are the two events mutually
exclusive or not mutually exclusive?
*In everyday life, there are events that cannot happen at the same time. We called
these mutually exclusive events.
* Because mutually exclusive events cannot happen together, the probability that both
events will happen together is equal to zero.
*If two events, A and B, are mutually exclusive, then the probability that either A or B
occurs is the sum of their probabilities. In symbols,
𝑷(𝑨 𝐨𝐫 𝑩) = 𝑷(𝑨 ∪ 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) Using the Venn diagram, we have,
Examples:
1. Pearl plans to visit her grandmother next week. If she chooses a day of the week at
random, what is the probability that she will choose Monday or Thursday?
Solution:
P(Monday or Thursday) = P(Monday) +P(Thursday)
P(Monday or Thursday) = 1/7 +1/7
P(Monday or Thursday) = 2/7
∴The probability of choosing a Monday or a Thursday is 2/7.

3. 2. In this ‘new normal situation’, nobody can go out without wearing a face mask. Mark
has 15 disposable face masks: 4 are red, 6 are blue and 5 are green. What is the
probability that he will wear a red or a blue face mask today?
Solution: A face mask cannot be both red and blue at the same time, so these are
mutually exclusive events.
𝑃(red or blue) = 𝑃(red) + 𝑃(blue)
𝑃(red or blue) = 4/15 + 6/15
𝑃(red or blue) = 10/15 or 2/3
∴The probability of wearing a red or a blue face mask is 2/3.
*Not mutually exclusive events are events that can happen at the same time.
If two events, A and B, are not mutually exclusive, then the probability that either A or
B occurs is the sum of their probabilities decreased by the probability of both occurring.
In symbols, 𝑷(𝑨 𝐨𝐫 𝑩) = 𝑷(𝑨 ∪ 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) – 𝑃(𝐴 ∩ 𝐵)
Using the Venn diagram, we have,
Examples:
1. If two standard dice are rolled, what is the probability of rolling doubles or a total of
10?
Solution:
Let: A = { rolling doubles} and B = {total of 10}
A = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)} B = {(5,5),(4,6),(6,4)}
P(𝐴) = 6/36 P(𝐵) = 3/36 𝐴 ∩ 𝐵 = 1/36
𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)
𝑃(𝐴 ∪ 𝐵) = 6/36 +3/36 – 1/36
𝑃(𝐴 ∪ 𝐵) = 8/36 or 2/9
∴The probability of rolling doubles or a total of 10 is 2/9 .
2. A card is drawn at random from a standard deck of 52 cards. Find the probability of
drawing a 7 or a red card?
Solution:
Let: A = { a 7} and B = {red card}
P(A)= 4/52 P(B)= 26/52 P( A ∩ B) = 2/52
𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)
𝑃(𝐴 ∪ 𝐵) = 4/52 + 26/52 – 2/52
𝑃(𝐴 ∪ 𝐵) = 30/52 -2/52
𝑃(𝐴 ∪ 𝐵)= 28/52 0r 7/13
3. If there is 40% chance that Jericho will buy a tablet, 70% chance that he will buy a
cellphone, and 28% chance that he will buy a tablet and a cellphone, what is the
probability that he will buy a tablet or a cellphone?
Solution:
Let: A = { % will buy tablet} and B = {% will buy cellphone}
P(A)= 40% P(B)= 70% 𝑃(𝐴 ∩ 𝐵= 28%
𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)
𝑃(𝐴 ∪ 𝐵) = 40% + 70% – 28%
𝑃(𝐴 ∪ 𝐵) = 82%
C. Engagement LEARNING TASK 3:
Tell whether each of the following situations indicates mutually exclusive events or not
mutually exclusive events and determine the probability of each event.
A box contains 26 balls labelled by each letter of the English alphabet. Assume that
each ball is designated by a unique letter and a ball is drawn randomly from the box,
what is the probability that it is
a) A or B?
b) E or a vowel?

4. c) P or a consonant?
d) O or a consonant?
e) a vowel or a consonant?
.
LEARNING TASK 4: Fair Play
Daryll and Ricky decided to play Polynomial Damath to ease their boredom brought
about by the COVID-19 pandemic. They agreed that they will roll a die to determine
who will make the first move. Both will roll the die and whoever gets the higher
number makes the first move. Ricky rolls the die and gets a 4. What is the probability
that Daryll gets to play first?
What number may turn up on the die if Daryll will roll it so that he will be the one to
play first?
D. Assimilation ***In what ways can you visually represent mutually exclusive and not mutually
events? In what situations are these effective or ineffective?
Asynchronous Activity
At a particular Junior High School, the number of students in the four grade levels
are broken down by percent, as shown in the table:
A single student is picked randomly by lottery for a cash assistance to be given due
to COVID-19.
a. What is the probability that the student selected for the cash assistance is a grade
7, a grade 8 or a grade 9?
b. Is the process of selecting a recipient for the cash assistance fair? Why or why
not?
c. Can you suggest another way of selecting the recipient for the cash assistance?
(According to Seif (2021), In a research-based learning approach, students actively search for and then
use multiple resources, materials, and texts in order to explore important, relevant, and interesting
questions and challenges.)
V. REFLECTION The learners, in their notebook, journal or portfolio will write their personal insights about the
lesson using the prompts below.
I understand that____________
I realized that_______________
“Reflection encourages learners to take charge of their own learning. It builds stronger
connections between learning experiences (Cross,2018).”
I believe that by doing this reflection, the students will be better able to see the importance of
their learning and how it might apply to their everyday lives.
Prepared by:
KAYCEE D. BALABAG
Teacher III