School Tucdao National High School Grade Level 11
Teacher Sung Shin Woong-ill A. Cipriano Learning Area Statistics and
Probability
Time & Date 10:30-11:30 am Feb. 12, 2024 Quarter 3rd
I. OBJECTIVES
A. Content Standards The learner demonstrates understanding of
key concepts of random variables and
probability distributions.
B. Performance Standards The learner is able to apply an appropriate
random variable for a given real-life
problem (such as in
decision making and games of chance).
C. Learning Competencies Constructs the probability mass function of
a discrete random variable and its
corresponding histogram. M11/12SP-IIIa-5
II. CONTENT Random Variables and Probability
Distributions
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide pages Commission on Higher Education.
(2016).Teaching Guide for Senior High
School Statistics and Probability. (pp. 120-
124)
2. Learner’s Material pages Department of Education. (2020). Learner’s
Material Statistics and Probability. (1st Ed).
pp. 49-51
3. Textbook pages Rohatgi, V. K., & Saleh, E. A.K. (2001). An
Introduction to Probability and Statistics (2nd
Ed.). A Winey-Interscience Publication. (pp.
52-55.)
De Veau, R. D., Velleman, P. F., and Bock,
D. E. (2006). Intro Stats. Pearson Ed. Inc.
Workbooks in Statistics 1: 11th Edition,
Institute of Statistics, UP Los Baños,
College
Laguna 4031
4. Additional Materials from NONE
Learning Resource (LR)
Portal
B. Other Learning Resources Two Coins, One Die
IV. PROCEDURE
A. Review Routine
Prayer
Checking of attendance
Checking of assignment if there is
Typography Legend:
Teacher’s statements are in Italic.
Learner’s response is in BOLD.
Review
Lesson from Previous Grading Period
How do you denote the probability of
event X happening? “P(X)”
How do you denote the probability of
event X NOT happening? “P(X’)”
How do you denote the probability of
event X OR Y happening? “P(X ∪
Y)”
How do you denote the probability of
event X AND Y happening? “P(X ∪
Y)”
Lesson from Previous Session
How do you draw a bar chart?
“To draw a bar chart:
1. Determine how many bars you
need based on your data set.
2. Choose a scale for your bars.
3. Sketch out rough outlines for the
bars and label them.
4. Use a ruler to ensure the bars are
straight and even in width.”
Excellent.
B. Motivation
Imagine you are at the gate of Tucdao
National High School and you ask a
motorcycle driver how much is the fare to
(A) Anywhere in Tucdao, Kawayan, Biliran
(P10)
(B) Anywhere in Brgy. San Lorenzo (P15)
(C) Anywhere in Brgy. Inasuyan. (P20)
(D) Anywhere in Sitio Tubig (P20)
(E) Anywhere in Brgy. Salvacion (P40)
It seems that you are experienced in
travelling the area.
Now, how can you better represent such
distribution of fares?
C. Activity Observe the following tables, histograms,
and functions.
Table 1. Outcome of flipping one coin
Coin Flip Heads Tails
Outcome
(x)
Probability 1/2 1/2
(X=x)
Histogram
Probability
1/2
0
Tails
Heads Tails
Outcome
Probability Mass Function:
½ if x = Heads, Tails
P(X=x) = 0, otherwise
Table 2. Outcome of rolling a die
.
Die Roll 1 2 3 4 5 6
(y)
Probabilit 1/ 1/ 1/ 1/ 1/ 1/
y (X=y) 6 6 6 6 6 6
Histogram
6/6
5/6
Probability
4/6
3/6
2/6
1/6
0
1 2 3 4 5 6
Outcome
Probability Mass Function:
1/6 if y = 1, 2, 3,
P(X=y) = 4, 5, 6
0, otherwise
Table 3. Outcome of flipping two coins
simultaneously
Flip Two HT H&T TT
Coins
Probabilit 1/4 2/4 1/4
y
(X=z)
Histogram:
Probability
4/4
3/4
2/4
1/4
0
HH H&T TT
Outcome
Probability Mass Function:
1/4 if z = HH, TT
P(X=z) = 2/4 if z = H & T
0, otherwise
D. Analysis These are the questions for Table 1.
1. Why is the probability of heads in
a coin flip equal to 1/2? (Because in
a coin flip, heads can only happen
once out of the two possible
outcomes.)
2. Why is the probability of a tails in
a coin flip equal to 1/2? (Because in
a coin flip, tails can only happen
once out of the two possible
outcomes.)
3. Note the part of a Probability
Mass Function(PMF) that says
“P(X=x) is ½ if x = Heads, Tails”.
What does it mean? (It means that
the probability is ½ for an
outcome of heads in a coin flip, so
as with tails.)
5. Note the part of a Probability Mass
Function(PMF) that says “P(X=x) is
0, otherwise. What does it mean? (It
means that the outcome other
than Heads, or Tails in a coin flip
is zero.)
These are the questions for Table 2.
1. Why is the probability of an
outcome in a die roll equal to 1/6?
(Because in a die roll, there is only
one outcome out of six possible
outcomes.)
2. Note the part of a Probability
Mass Function(PMF) that says
“P(X=y) is 1/6 if x = 1, 2, 3, 4, 5, or
6”. What does it mean? (It means
that the probability is 1/6 any side
outcome of a die roll.)
3. Note the part of a Probability
Mass Function(PMF) that says
“P(X=x) is 0, otherwise. What does it
mean? (It means that the outcome
other than 1, 2, 3, 4, 5, or 6 in a die
roll is zero.)
These are the questions for Table 3.
1. Why is the probability of an
outcome of HH, or TT in flipping two
coins simultaneously equal to 1/4?
(Because each outcome can only
occur once in flipping two coins
simultaneously.)
2. Why is the probability of an
outcome of H & T in flipping two
coins simultaneously equal to 2/4?
(Because the outcome H & T can
occur twice in flipping two coins
simultaneously.)
3. Note the part of a Probability
Mass Function(PMF) that says
“P(X=x) is 0, otherwise. What does it
mean? (It means that the outcome
other than 1, 2, 3, 4, 5, or 6 in a die
roll is zero.)
Last meeting, we made bar graphs.
What is the difference between bar
graphs and histograms? (There are
two key differences. One is for
histograms; consecutive bars
have no spaces. And second, the
lower and left part of the axis is
starts with zero.)
Good observation.
E. Abstraction 1. How do you construct a histogram of
a discrete random variable? (First,
understand the data and
determine a suitable bin width.
Then, organize the data into bin
ranges and frequencies. Next,
label the axes and write the title.
Finally, plot the histogram)
2. How do you construct the probability
mass function of a discrete random
variable? (First, determine the
possible outcomes. Then,
calculate their probabilities, Next,
group outcomes with similar
probabilities. Finally, write them in
function form.)
F. Application In the game monopoly, two dice are rolled
simultaneously.
Create a table for the possible outcomes of
rolling two dice simultaneously.
Next, construct a histogram to represent the
probability of outcomes.
Finally, construct a Probability Mass
Function (PMF) to represent the probability
of outcomes.
G. Assessment/Evaluation There is a local game called “hantak” where
players flip three coins simultaneously.
(Optional: Create a table of probabilities for
flipping three coins simultaneously.)
Construct a histogram to represent the
probability of outcomes. (10 pts, -1 pt. for
each incorrect part)
Then, Probability Mass Function (PMF) to
represent the probability of the outcomes.
(5 pts, -1 pt. for each incorrect part.)
H. Assignment/Additional Activities Read about computing probabilities
corresponding to a given random variable.
V. Remarks
VI. Reflection
A. No. of learners who earned 80%
on the formative assessment
B. No. of Learners who require
additional activities for
afaqbhfafabaqbfaff1fremediation
.
C. Did the remedial lessons work?
No. of learners who have caught
up with the lesson.
D. No. of learners who continue to
require remediation
E. Which of my teaching strategies
worked well? Why did these
work?
F. What difficulties did I encounter
which my principal or supervisor
can help me solve?
G. What innovation or localized
materials did I use/discover
which I wish to share with other
teachers?
