DETAILED LESSON PLAN
School Division:
ANTIQUE
School:
SAN PEDRO NHS
Teacher:
JENNY C. GALONO
Grade
Level:
Learning
Area:
Quarter:
10 - EMERALD
MATHEMATICS
THIRD
Date
I. OBJECTIVES
A. Content Standard
The learner demonstrates understanding of key concepts of combinatorics and probability.
B. Performance Standard
The learner is able to use precise counting technique and probability in formulating conclusions
and making decisions.
C. Learning Competencies
The learner illustrates the probability of mutually exclusive events.
(M10SP-IIIi-1)
At the end of the lesson, the students will be able to:
1. determine what is mutually exclusive events and not mutually exclusive events
2. find the probability of mutually exclusive events and not mutually exclusive events
3. participate actively in the class discussion
With 80% proficiency.
II. CONTENTS
Probability of Mutually Exclusive Events and Not Mutually Exclusive Events
III. LEARNING
RESOURCES
A. References
Mathematics Learner’s Module for Grade 10 pp. 301-316
Mathematics Teacher’s Module for Grade 10 pp. 291-293
B. Other Learning
Resources
Power point Presentation, White Board, White Board Marker, Manila Paper, Construction Paper
C. Duration
IV. PROCEDURES
1 hour
Teacher’s Activity
Student’s Activity
1. Greetings
Good Morning class!
Good Morning Ma’am!
2. Prayer
Student 1, please lead the prayer.
You can now take your seats.
3. Checking of Attendance
Let’s check your attendance.
Student 1 leads the prayer.
Please say present when I call your name.
Okay now, please pass your assignment from our
last meeting.
Review
A. ELICIT
(5 minutes)
Before anything else, let’s recap what you have
learned last meeting.
If it is events that cannot happen or occur at the same Mutually Exclusive Events
time, what kind of event it is?
Very good.
How about the events that can happen or occur at the
same time?
Not Mutually Exclusive Events
Very good.
B. ENGAGE
(10 minutes)
What is our formula in finding the probability of
mutually exclusive events?
P(A or B) = P(A) + P(B)
How about the formula in finding the probability of
not mutually exclusive events?
Very good!
P(A or B) = P(A)+P(B)- P(A and B)
Motivation
Now first, let’s have a game.
This game is called “MUTUALLY EXCLUSIVE OR
NOT?”
This will be a group work and you will be 2 groups.
Consider each problem presented. Draw a Venn
diagram for each. Determine whether the events are
mutually or not mutually exclusive. Then, find the
probability.
For this group activity, there will 1 representative in
each group to draw the Venn diagram, 1 to write if it
is mutually or not and 1 who will solve the probability
of the events.
For the group 1 problem.
1. Mario has 45 red chips, 12 blue chips, and 24,
white chips. What is the probability that Mario
randomly selects a red chip or a white chip?
For the group 2 problem.
2. Of 240 students, 176 are on the honor roll, 48 are
members of the varsity team, and 36 are in the honor
roll and are also the members of the varsity team.
I will give you 5 minutes to answer in group and then
after that, you may write your answers in the board.
And your time’s start now.
Time’s up!
What do you feel when doing the activity?
How can you tell that the problem given to your
group is mutually exclusive? Not mutually exclusive?
Wow, very good!
This morning, we will continue our lesson all about
Mutually and Not Mutually Exclusive Events.
But before going through that topic, this is our goals
for today.
At the end of the lesson, you will be able to:
1. determine what is mutually exclusive events and
not mutually exclusive events
2. find the probability of mutually exclusive events
and not mutually exclusive events
3. participate actively in the class discussion
With 80% proficiency.
C. EXPLORE
(5 minutes)
Let’s have an activity.
This will be now an individual activity.
Activity: Mutually Exclusive or not?
Consider each problem presented. Draw a Venn
diagram for each. Determine whether the events are
mutually or not mutually exclusive. Then, find the
probability.
1. Ruby’s dog has 8 puppies. The puppies include
white females, mixed-color females, 1 white male,
and 2 mixed-color males. Ruby wants to keep 1
puppy that is female and white?
2. Carl’s basketball shooting records indicate that for
any frame, the probability that he will score in a twopoint shoot is 30%, a three-point shoot, 45%, and
neither, 25%. What is the probability that Cindy will
score either in a two-point shoot or in a three-point
shoot?
D. EXPLAIN
(Reporting)
(5 minutes)
If you’re done answering, please write your answer
on the board and explain your answer.
Student 5, you may come to the front and write your
answer in number 1.
Student 2 for number 2.
And student 7 for number 3.
Very good class!
E. EXPLAIN
(5 minutes)
F. ELABORATE
(Generalization)
(10 minutes)
What have you noticed about the activity that we
have?
If it is events that cannot happen or occur at the same Mutually Exclusive Events
time, what kind of event it is?
Very good.
How about the events that can happen or occur at the Not Mutually Exclusive Events
same time?
Very good.
In our activity, for the problem number 1.b, the event
of getting a 5 and getting a number divisible by 3
from the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,
14, 15} are mutually exclusive events.
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) + P(B)
Example: P(getting a 5 or getting a number divisible
by 3) = P(1)+P(5) = 6/15
Any clarifications?
None Ma’am
Okay, then for the event of getting a number
divisible by 3 or the event of getting a number
divisible by 4 in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12, 13, 14, 15} is not mutually exclusive events.
It is because that the subset of numbers divisible by
3 contains an element which is also a subset of the
numbers divisible by 4.
If two events 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)+P(B)- P(A and B)
Example: P(getting a number divisible by 3 or
getting a number divisible by 4) = P(5)+P(3) – P[(1)
= 7/15
Any clarifications?
None Ma’am
Now, what do you call the events that cannot happen Mutually Exclusive Events
or occurs at the same time?
Very good.
How about the events that can happen or occur at the Not Mutually Exclusive Events
same time?
Very good.
How do you illustrate mutually exclusive events?
P(A or B) = P(A) + P(B)
Very good.
Then how about the symbol of not mutually P(A or B) = P(A)+P(B)- P(A and B)
exclusive events?
Very good.
G. EVALUATE
(5 minutes)
Now, get a 1 whole sheet of paper and answer the
following questions.
More Exercises on Mutually exclusive and Not
Mutually Exclusive Events
1. A restaurant services a bowl of candies to their
customers. The bowl of candies Gabriel receives has
10 chocolates candies, 8 coffee candies, and 12
caramel candies. After Gabriel chooses a candy, he
eats it.
Find the probability of getting candies with the
indicated flavors.
a. P(chocolate or coffee)
b. P(caamel or not coffee)
c. P(coffee or caramel)
d. P(chocolate or not caramel)
2. Rhian likes to wear colored shirts. She has 15
shirts in the closet. 5 of these are blue, 4 are in
different shade of red, and the rest are of different
colors. What is the probability that she will wear a
blue or a red shirt?
3. Mark has pairs of pants in 3 different colors, blue,
black, and brown. He has 5 colored shirts: a white, a
red, a yellow, a blue, and a mixed-colored shirt.
What is the probability that Mark wears a black pair
of pants and a red shirt on a given day?
4. A motorcycle license plate has 2 letters and 3
numbers. What is the probability that a motorcycle
has a license plate containing a double letter and
even numbers?
H. EXTEND
(5 minutes)
For your assignment, consider the problems given.
Draw a venn diagram for each. Determine whether
the vents are mutually exclusive or not mutually
exclusive, then find the probability.
1. Mario has 45 red chips, 12 blue chips, and 24,
white chips. What is the probability that Mario
randomly selects a red chip or a white chip?
2. Of 240 students, 176 are on the honor roll, 48 are
members of the varsity team, and 36 are in the honor
roll and are also the members of the varsity team.
3. Ruby’s dog has 8 puppies. The puppies include
white females, mixed-color females, 1 white male,
and 2 mixed-color males. Ruby wants to keep 1
puppy that is female and white?
4. Carl’s basketball shooting records indicate that for
any frame, the probability that he will score in a twopoint shoot is 30%, a three-point shoot, 45%, and
neither, 25%. What is the probability that Cindy will
score either in a two-point shoot or in a three-point
shoot?
V. REMARKS
VI. REFLECTION