Grade 10 (Statistics and Probability)
1st Classroom
Observation
“Dependent and Independent Events”
CONTENT STANDARD: The learner demonstrates understanding of key concepts of combinatory
and probability.
PERFORMANCE STANDARD: The learners are able to use precise counting technique and
probability in formulating conclusions and making decisions.
LEARNING COMPETENCY: The learners are able solves problems involving probability.
(M10SP-IIIi-j-1)
I. OBJECTIVES/TARGET OF THE LESSON
At the end of the lesson, the learners are expected to:
1. differentiate dependent from independent events,
2. solve the probability of dependent and independent events; and
3. cite a significant application of computing the probability of dependent and independent events
in real life.
II. SUBJECT MATTER/CONTENT AND MATERIALS
Topic: Dependent and Independent Events
Learning resources:
A. References: Grade 10 Mathematics Teacher’s Guide, pp. 296 - 300
Grade 10 Mathematics Learner’s Module, pp. 341 - 345
Exploring Mathematics 10 by Baccay, Elisa S., et.al., pp. 333–338
B. Other Learning Resources: www.tutorVista.com
C. Pre-requisite concept: Mutually and non-mutually exclusive events
D. Instructional Materials: Blackboard, Chalk, Enlarged Images/visual Aids, Activity Sheet,
Rubric, Calculator and Peso Coins.
E. Skills to Develop: Knowing and Understanding, computing and solving, applying
and connecting.
F. Values Integration: Accuracy, objectivity, and perseverance, honesty.
G. Subjects to be integrated: English, Filipino, P.E., ESP
H. Math Concepts:
The study of probability mostly deals with combining different events and studying these
events alongside with each other. How these different events relate to each other
determines the methods and rules to follow when we’re studying their probabilities.
Events can be divided into two major categories, dependent and independent events.
Independent Events – the occurrence of one of the events gives us no information about
whether or not the other event will occur; that is, the events have no influence on each other.
Dependent Events – when the outcome of one event affects the outcome of another event or the
probability of one event occurring influences the likelihood of the other event.
I. Methodology: 7 E’s of Learning (Elicit, Engage, Explore, Explain, Elaborate, Evaluate, Extend)
III. PROCEDURE
Time
Frame
5 mins
Teacher’s Hint
Teacher’s Activity
Instructional
Materials
Student’s Activity
A. Preliminary
Activities
1. Greetings
Good afternoon class!
Good afternoon sir!
2. Prayer
May I request everyone to please (the students will pray the
stand and let us pray.
interfaith prayer)
3. Securing the
cleanliness
and
orderliness of
the classroom
Before you take your seat, please (students will arrange their chairs
arrange your chairs properly and and will pick-up all the pieces of
pick-up all the pieces of paper paper)
under your chair.
4. Checking the Class joyful, kindly checks the (class joyful will check
attendance
attendance of your classmate.
attendance of the class)
5. House Rules
the
Glad to hear that that only few are
absent! May I remind everyone of
the things we need to remember
during our MATH Time.
Maintain proper behavior.
Actively participate.
Time conscious.
Help others; ask for Help.
COT Indicator No. 5: Managed
learner behavior constructively
by applying positive and nonviolent discipline to ensure
learning-focused environments.
Annotation:
The teacher imposed house rules
“MATH” before the start of the new
lesson which will be followed by the
students throughout the whole
period for the smooth flow of the
discussion.
ELICIT
5 mins
Checking of
assignment
Let us check the assignment
(the students will exchange their
assignment)
Enlarged
You randomly choose a card from
a standard deck of 52 playing
cards, find the probability of getting:
1. a 9 or a king
2. an ace or a spade
3. a face card or a diamond
4. a jack or a queen
5. a face card or a black card
2 mins
Images/
visual
Aids
1. 2/13
2. 4/13
3. 11/26
4. 2/13
5. 8/13
Recall/Review
Last meeting, we tackled about,
mutually and non-mutually
exclusive events.
So, who can recall what mutually Sir! Two events A and B are said
exclusive event is?
to be mutually exclusive if they
cannot occur at the same time.
That’s right!
We said that the two events are
mutually exclusive if they cannot
occur at the same time. Or we can
also said that this events are
disjoint which means that the
probability of them both occurring
at the same time is 0.
Say for example, Neric will going
forward and backward.
The first thing he can do is to move
forward first or to move backward.
He can’t do both at the same time.
How about the non-mutually Sir!
Non-mutually
exclusive
exclusive events?
events, if two events A and B can
occur on the same time
Excellent!
Non-mutually exclusive events are
events that can both be true at the
same time. Or we can say that it is
the opposite of mutually exclusive
events.
For example, Neric will move
forward while laughing. Moving
forward and laughing happened at
the same time. So, that’s a nonmutually exclusive event because
both events can be true.
How can you solve for the
probability of the 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)
How about for the non-mutually If two events, A and B, are
exclusive events?
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)
Good job class!
It seems that you are now ready for
our next lesson.
7mins
ENGAGE
But, before that let’s have first a
game.
Our game is called,
“Tails Never Fails”
On this game, your luck and
honesty will be tested.
So to guide you in playing this
game, here are the following
mechanics:
MECHANICS
1. The teacher will choose 15 (The students will listen to the Peso
participants to join the game. teacher as he reads the coins
Others will observe the game.
mechanics of the game)
2. All participants will form one
big circle.
3. Each participant will get one
peso coin and sit like Indian
style on the floor.
4. On a count of three, all
participants will flip their coin in
a moderate level.
5. A participant/s that landed their
coin head will be eliminated
and those who landed tail will
remain on the game.
6. The process of the game will
continue until there’s only five
or less participants remain.
7. Those who remain on the
game will be the winner and
will gain a prize.
Are you ready class?
Yes sir!
Let the game begins!
(the students will play the game )
How did you find our game class?
(students will answer)
What do you think is the chance
that the coin will landed tail?
It’s ½ or 50% sir because there’s
only two possible outcomes.
Very good!
Head or tail
COT Indicator No. 1: Applied
knowledge of content within and
across
curriculum
teaching
areas.
Annotation:
The teacher integrate game
which is a part of the physical
education concept and also apply
the virtue of honesty in the ESP in
conducting the activity.
12
mins.
B. Lesson
Proper
1. Presentation
of the lesson
In the game, all of you flipped a Yes sir!
coin right?
Among of you, who only flipped
their coin twice?
So, on your first attempt in flipping
a coin, you got tail right?
(the students who only flipped
their coin twice will raise their
hand)
Yes sir!
When you flipped your coin on the No sir. Because when you flipped
second time, does the result affect a coin, the possible result can
by the outcome on the first?
either be head or tail.
Very Good!
On the game we conducted, the
first round of our game consists of
15 participants.
On the second round, how many
students remained?
Only 10 students remained.
And on the third round, only five Yes sir!
students remained on the game
and declared to be the winners
right?
In every round, does the chance
that Dustine will be one of the five
students who remained on the
game will be affected?
Okay, based on the observation of Sir, it is all about Independent
the game you played, What do you and Dependent Events
think is our lesson for today?
Discussion
Correct!
The events are independent if
the occurrence of one of the
events gives us no information
about whether or not the other
event will occur; that is, the
events have no influence on
each other. While, when the
outcome of one event affects the
outcome of another event, then,
they are dependent events.
Okay, I will give situations and you
are going to tell whether it is
independent or dependent events.
Are you ready?
Yes, sir!
Who has an idea of what is the
difference between independent
and dependent events?
1. Flipping a coin and rolling a
die
2. Reading books and
Increasing of English
vocabulary
3. Drawing 2 red cards
without replacement of the
first card
4. Drawing 2 face card with
replacement of the first
card
5. Eating healthy foods and
washing clothes
1. Independent events
2. Dependent events
Enlarged
Images/
visual
Aids
Enlarged
Images/
visual
Aids
3. Dependent events
4. Independent events
5. Independent events
Very Good!
Who can recall about conjunction
in your English class?
There are 7 coordinating
conjunctions and you can
remembered using the acronym
FANBOYS. (for, and, nor, but, or,
yet, so). In your Filipino, it is called
pangatnig/pang-ugnay.
A conjunction is a word used to
connect words, phrases and
clauses.
As you observe class, the
conjunction that is used in the
independent and dependent event
is “AND” while in our previous
lesson about mutually and not
mutually exclusive events, the
conjunction was “OR”
Yes, sir!
Agree?
Now, how we will be able to find
the probability of Independent
events?
If two events, A and B, are
independent, then the probability
of both events occurring is the
product of the probability of A
and the probability of B. In
symbols,
P (A and B) = P (A) • P (B)
If two events, A and B, are
Enlarged
Images/
visual
Aids
How about the probability of
dependent events?
For Example,
dependent, then the probability
of both events occurring is the
product of the probability of A
and the probability of B after A
occurs. In symbols,
P (A and B) = P (A) • P (B following A)
Let us try to find the probability of
the given problem below:
A jar of marbles contains 4
blue marbles, 5 red marbles,
3 green marble, and 2 black
marbles. A marble is chosen at
random from the jar. After
replacing it, a second marble is
chosen. Find the probability of
drawing green and red marbles.
How about if there is no
replacement of the first marble,
what is the probability of drawing
both green marbles?
P(green and red marbles) =
P(green marbles) •
P(red marbles) = 3/14 • 5/14
= 15/196
Enlarged
Images/
visual
Aids
P(green and green marbles) =
P(green marbles) •
P(green/green marbles)
= 3/14 • 2/13
= 6/182 or 3/91
Do you have any question about
dependent
and
independent
events?
Superb!
It seems that you really understand
the concept of dependent and
independent events.
COT Indicator No. 1: Applied
knowledge of content within and
across
curriculum
teaching
areas.
Annotation:
The teacher applies English &
Filipino lessons in introducing the
lesson.
COT Indicator No. 3: Applied a
range of teaching strategies to
develop critical and creative
thinking, as well as other higherorder thinking skills.
Annotation:
The teacher asked HOTS
questions in the lesson part from
the presentation of the lesson to
the discussion like “HOW”
10
mins.
EXPLORE
a. Pre-activity
For your activity,
I will divide you into three groups.
You will count 1 – 4.
(the student will do the task)
Those who had the same number
belong to the same group.
Each group will be given an activity
sheet. It contains tasks to be done
by the group. I will give you
Activity
sheet
5minutes to finish the task.
You need to choose a leader and a
member. The chosen member will
be the in-charge of writing your
solutions on the board. The leader
will act as the group facilitator and
at the same time the one who will
explain your output.
Rubric
Here are the rubrics in grading your
group output:
CRITERIA:
Accuracy –
4
Cooperation –
2
Time Management – 2
Presentation –
2
TOTAL:
10 POINTS
Are you now ready to perform the
group activity?
Yes sir!
Okay, your time start now!
b. Activity proper
Group 1:
(the
students
will
do
Consider a box that contains 14
activity)
red balls,12 blue balls, and 9
yellow balls. A ball is drawn at
random and the color is noted and
then put back inside the box.
Then, another ball is drawn at
P(blue and blue balls)
random. Find the probability that:
= 12/35 • 12/35
= 144/1225
both are blue
the
Group 2:
Consider a box that contains 14
red balls,12 blue balls, and 9
yellow balls. A ball is drawn at
random and the color is noted and
then put back inside the box.
P(red and yellow balls)
Then, another ball is drawn at
= 14/35 • 9/35
random. Find the probability that:
= 126/1225 or 18/175
the first is red and the
second is yellow
Group 3: Consider a box that
contains 14 red balls, 12 blue
balls, 9 yellow balls. Suppose that
two balls are drawn one after the
other without putting back the first
ball. Find the probability that:
both are blue
Group 4: Consider a box that
contains 14 red balls, 12 blue
balls, 9 yellow balls. Suppose that
two balls are drawn one after the
other without putting back the first
ball. Find the probability that:
the first is red and the
second is yellow
COT Indicator No. 4: Managed
classroom structure to engage
learners, individually or in
P(blue and blue balls)
= 12/35 • 11/34
= 132/1190 or 66/595
P(red and yellow balls)
= 14/35 • 9/34
= 126/1190 or 9/85
groups,
in
meaningful
exploration,
discovery
and
hands-on activities within a
range of physical learning
environment.
5
mins.
EXPLAIN
c. Post activity
Annotation:
In performing the activity, the
teacher will monitor the behavior of
the learners towards their fellow
group mates and ensure that the
instructions and the criteria in the
rubrics are strictly follow.
So now, each representative on (each representative will present
each group will now present their their output)
output.
The teacher will supplement/
explain further the presentation of
the students.
Bravo class!
You
all
did
presentation.
an
excellent
All group performed well in the
activity. Give yourself a round of
applause!
(students will clap their hands)
In your activity, how did you We base from the definition of
and
independent
determine whether the given dependent
scenario
is
dependent
or events sir.
independent events?
Good job!
Based from the definition of
dependent
and
independent
events, you can easily determine
whether an event is dependent or
independent.
How about in computing the Sir, we just follow the formula for
probability of dependent and computing the probability of
dependent
and
independent
independent events?
events. Just multiply the event of
first and second for independent.
Magnificent!
COT Indicator No. 2: Used
ranged of teaching strategies
that
enhance
learner
achievement in literacy and
numeracy skills.
Annotation:
The teacher utilized varied
teaching strategies in teaching the
concepts to enhance the literacy
and numeracy skills of the learners
like inductive, the use of game,
discovery, cooperative learning,
problem solving and discussion.
And for dependent events,
multiply the events of the first to
the event of the second after the
first event occur.
3 mins
ELABORATE
Again class, what is the difference The events are independent if
between
independent
and the occurrence of one of the
dependent events?
events gives us no information
about whether or not the other
event will occur; that is, the
events have no influence on
each other. While, when the
outcome of one event affects the
outcome of another event, then,
they are dependent events.
That’s right!
Independent events are the
opposite of dependent events.
So, what is the basis for Sir, if the given problem has an
determining whether events are statement of “replaced” then it is
dependent or independent?
independent, but if it has “did not
replaced” then it is dependent.
Very good!
5 mins APPLY
The word “replaced” and “did not
replaced can be the hint to
determine the dependent and
independent events.
So, how would you use the concept For example sir, you join a raffle
of probability of dependent and draw. We can know our chances
independent events in real life?
of winning on the raffle draw by
applying
the
concept
of
dependent events.
That’s right!
We can determine the probability of
winning the raffle draw by applying
the concept of our topic this day.
So who can solve this problem?
(students will answer)
A random sample of parts coming
off a machine is done by an
inspector. He found that 5 out of
100 parts are bad on average. If he
were to do a new sample, what is P(bad part & bad part)=P(bad
the probability that he picks a bad part)*P(bad part / bad part)
part and then, picks another bad
=5/100x4/99
part if he doesn’t replace the first?
= 1/495
Excellent class!
It seems that you really understand
our topic this afternoon.
COT Indicator No. 6: Used
differentiated, developmentally
appropriate learning experiences
to address learners’ gender,
needs, strengths, interests and
experiences.
Annotation:
The teacher utilized varied
teaching in every part of the lesson
like inductive, the use of game,
discovery, cooperative learning,
problem solving and discussion to
address learners’ gender, needs,
strengths,
interests
and
experiences
IV. EVALUATE:
Directions: Distinguish the following events if it is a dependent event or an independent event. Write DE if the
event is a dependent, and IE if the events are independent.
_________1. Turning off the lights and winning the lottery.
_________2. Killing a person and going to jail.
_________3. Winning a contest and a dog barking.
_________4. Singing a high tone note and having a typhoon.
_________5. Drinking an alcohol and getting drunk.
Directions: Answer the following problems.
1. A bag of jelly beans contains 10 red, 6 green, 7 yellow, and 5 orange jelly beans. What is the probability
of randomly choosing a red jelly bean, replacing it, and then randomly choosing an orange jelly bean?
2. Rene and Cris went to a grocery store to buy drinks. They chose from 10 different brands of juice drinks,
6 different brands of carbonated drinks, and 3 different brands of mineral water. What is the probability that
Rene and Cris both chose juice drinks, if Rene randomly chose first and like the first brand he picked up?
V. EXTEND/ASSIGNMENT/ADDITIONAL ACTIVITIES FOR REMEDIAL AND ENRICHMENT
Directions: Solve the following:
1. A bag of beans contains 10 Patani seeds, 6 Kasoy seeds, 7 Cacao seeds, and 5 Langka seeds. What is
the probability of randomly choosing a patani seed, replacing it, randomly choosing another
patani, replacing it, and then randomly choosing a langka seed?
2. There are 6 black pens and 8 blue pens in a jar. If you take a pen without looking and then take
another pen without replacing the first, what is the probability that you will get 2 black pens?
3. What is Conditional Probability of an event?
VI. REMARKS:
VII. REFLECTION: