Stat. W2D2

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. 13, 2024 Quarter 3rd
I. OBJECTIVES
A. Content Standards The learner demonstrates understanding of key
concepts of random variables and probability
distributions.
B. Performance The learner is able to apply an appropriate random
Standards variable for a given real-life problem (such as in
decision making and games of chance).
C. Learning Computes probabilities corresponding to a given
Competencies random variable. M11/12SP-IIIa-6
II. CONTENT Random Variables and Probability Distributions
III. LEARNING RESOURCES
A. References
1. Teacher’s Guide Commission on Higher Education. (2016).Teaching
pages Guide for Senior High School Statistics and
Probability. (pp. 124-125)
2. Learner’s Material Department of Education. (2020). Learner’s Material
pages Statistics and Probability. (1st Ed). pp. 52-53
3. Textbook pages Rohatgi, V. K., & Saleh, E. A.K. (2001). An
Introduction to Probability and Statistics (2nd Ed.). A
Winey-Interscience Publication. (pp. 56-57.)
4. Additional Materials NONE
from Learning
Resource (LR)
Portal
B. Other Learning Two coins, 1 die
Resources
IV. PROCEDURE
A. Review Routine
 Prayer
 Checking of attendance
 Checking of assignment if there is
Review
Typography Legend:
Teacher’s Statements are in Italic.
Learner’s responses are in Bold.
Before we proceed to our lesson, let’s have a review
first.
How to you create a histogram? (First, understand

the data and select a preferred bin width. Then,
organize the data into bin ranges and
frequencies. Next, label the axes and write the
tile. Finally, plot the histogram)
You remembered well. Next question, 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.)
B. Motivation Imagine somebody is going to roll a die and if you

win in a die roll, you will be given a million pesos.
You are given two choices:
A. x < 3
B. y ≥ 4
Which of the two options would you chose?

C. Activity
Observe the table below.
Table 1. Inequality Symbols

Symbol Meaning Word Phrases
< Less than Fewer than,
Below
> Greater than More than,
Above
≥ Less than or At most, no
Equal to more than
≤ Greater than or At least, no
Equal to less than
≠ Not equal to Not equal to
What is the sample space of a die roll? {1, 2, 3, 4, 5,

6}
Let’s use that sample space to practice about

inequalities.
Let x be a random variable of a die roll. What are the

outcomes considered in the following expression?
1. x < 3? {1, 2}
2. x > 3? {4, 5, 6}
3. x ≤ 3? {1, 2, 3}
4. x ≥ 3? {3, 4, 5, 6}
5. x ≠ 3? {1, 2, 4, 5, 6}
Observe the following table.
Table 2. Random variable(x) and its Probability

x P(x)
1 1/6
2 1/6
3 1/6
4 1/6
5 1/6
6 1/6
Refer Table 2 to complete the following table.
Table 3. Probability of range of values of x.
Event (x) Outcomes Probability

x=3 {3} 1/6
x>3 {4, 5, 6} 3/6
x<3 {1, 2} 2/6
x≥3 {3, 4, 5, 6} 4/6
x≤3 {1, 2, 3} 3/6
x≠3 {1, 2, 4, 5, 6} 5/6
Expressed in another way, what is
1. P(x = 3)? {1/6}

2. P(x > 3)? {3/6}
3. P(x < 3)? {2/6}
4. P(x ≥ 3)? {4/6}
5. P(x ≤ 3)? {3/6}
6. P(x ≠ 3)? {5/6}
D. Analysis What is the difference between = and ≠? (The

equality sign includes the value on the right of
the sign from the list of possible outcomes. On
the other hand, the equality sign excludes the
value on the right of the sign from the list of
possible outcomes. )
What is the difference between < and ≤? The < sign

excludes the value on the right of the sign from
the list of possible outcomes. On the other hand,
the ≤ sign includes the value on the right of the
sign from the list of possible outcomes.
What is the difference between > and ≥? The > sign

excludes the value on the right of the sign from
the list of possible outcomes. On the other hand,
the ≥ sign includes the value on the right of the
sign from the list of possible outcomes.
E. Abstraction How do you compute the probabilities corresponding
to a given random variable?
(First, identify the reference quantity. Then,

determine the range of quantities included by the
equality or inequality sign. Next, count the
number of outcomes. Finally, compute the
probability.)
F. Application Try to answer the scenario I’ve given you at the start
of the session.
Imagine somebody is going to roll a die and if you

win in a die roll, you will be given a million pesos.
You are given two choices:
A. x < 3
B. y ≥ 4
Which of the two options offers greater chances of

winning?
G. Assessment/Evaluation Complete the following table. (1 pt per entry)
Table 1. Die Roll Outcomes

Event (x) Outcomes Probability
x=5
x>2
x<6
x≥4
x≤1
x≠6
H. Assignment/Additional Read about calculating the mean and variance of
Activities discrete 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
remediation.
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?

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School Tucdao National High School Grade Level 11

Teacher Sung Shin Woong-ill A. Cipriano Learning Area Statistics and

How to you create a histogram? (First, understand

You remembered well. Next question, how do you

B. Motivation Imagine somebody is going to roll a die and if you

Which of the two options would you chose?

Table 1. Inequality Symbols

What is the sample space of a die roll? {1, 2, 3, 4, 5,

Let’s use that sample space to practice about

Let x be a random variable of a die roll. What are the

Observe the following table.

Table 2. Random variable(x) and its Probability

Refer Table 2 to complete the following table.

Table 3. Probability of range of values of x.

Event (x) Outcomes Probability

Expressed in another way, what is

1. P(x = 3)? {1/6}

D. Analysis What is the difference between = and ≠? (The

What is the difference between < and ≤? The < sign

What is the difference between > and ≥? The > sign

(First, identify the reference quantity. Then,

Imagine somebody is going to roll a die and if you

Which of the two options offers greater chances of

Table 1. Die Roll Outcomes

A. No. of learners who

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