Republic of the Philippines
Department of Education
REGION I
SCHOOLS DIVISION OF THE CITY OF BATAC
ACTIVITY SHEETS IN
STATISTICS AND PROBABILITY
QUARTER III - WEEK 1
Most Essential Learning Competencies (MELCs):
1. illustrates a random variable (discrete and continuous) (M11/12SP-IIIa-1);
2. distinguishes between a discrete and a continuous random variable
(M11/12SP-IIIa-2);
3. finds the possible values of a random variable (M11/12SP-IIIa-3); and
4. illustrates a probability distribution for a discrete random variable and its
properties (M11/12SP-IIIa-4).
Prepared by:
JAMIEFEL P. PUNGTILAN
Teacher III
Background Information
Random Variable
It is a variable whose value is a numerical outcome of a random phenomenon.
It is denoted with a capital letter.
Example: X = {0, 1, 2, 3}
X could be 0, 1, 2, or 3 randomly
Types of Random Variables
Discrete Random Variable
It is a random variable that can only take a countable number of values.
Examples: Number of students in a classroom
Number of red marbles in a jar
Continuous Random Variable
It is a random variable which takes an infinite number of possible values. This
type of variable is usually measurements.
Examples: Distance traveled while walking
Temperature on a sunny day
Discrete Probability Distribution
The probability distribution of a discrete random variable X is a list of each
possible value of X together with the probability that X takes that value in one trial of
the experiment.
The probabilities in the probability distribution of a random variable X must
satisfy the following two conditions:
1) Each probability P(X) must be between 0 and 1 inclusive: 0≤P(X)≤1.
2) The sum of all the probabilities is 1: ΣP(X)=1.
Example: Suppose two coins are tossed and we are interested to determine the
number of heads that will come out. Let us use H to represent the number of heads
that will come out. Determine the values of the random variable H and construct its
probability distribution.
Step 1: List the sample space of the experiment.
S = {HH, HT, TH, TT}
Step 2: Count the number of random variable in each outcome and assign the number
to this outcome. Construct the frequency distribution of the values of the random
variable.
Outcomes Value of H
HH 2
HT 1
TH 1
TT 0
The values of the random variable H are 2, 1 and 0.
Step 3: Construct the probability distribution of the random variable by getting the
probability of occurrence of each value of the random variable.
Value of H P(H)
1
2 4
2 1
1 or 2
4
1
0 4
Note: Using the second property of discrete probability distribution, the sum of all the
probabilities is 1. That is:
1 2 1 4
+ + = =1
4 4 4 4
Name:___________________________________________ Date:____________
Grade/Section: ____________________________________Score:____________
Most Essential Learning Competencies:
• illustrates a random variable (discrete and continuous) (M11/12SP-IIIa-1)
• distinguishes between a discrete and a continuous random variable
(M11/12SP-IIIa-2)
Activity 1.1: Am I Discrete or Continuous?
Directions: Classify the following as discrete or continuous. Write
D for discrete or C for continuous on the space provided.
______ 1. Number of birds in a nest
______ 2. Number of winners in lotto for each month
______ 3. Capacity of the electrical resistors
______ 4. Voltage of radio batteries
______ 5. Amount of salt needed to bake a loaf of bread
______ 6. Capacity of an auditorium
______ 7. Number of mobile phones sold in one week in XY Store
______ 8. Length of wire ropes
______ 9. Length of sleeps of a baby in number of hours
______ 10. Speed of a car on a highway
Name:___________________________________________ Date:____________
Grade/Section: ____________________________________Score:____________
Most Essential Learning Competency:
• distinguishes between a discrete and a continuous random variable
(M11/12SP-IIIa-2)
Activity 1.2: Fill Me Up
Directions: Give five examples each of discrete and continuous
random variable.
Note: Examples copied from the net and similar to your
classmates will not be counted as correct.
Discrete Continuous
Name:___________________________________________ Date:____________
Grade/Section: ____________________________________Score:____________
Most Essential Learning Competencies:
• finds the possible values of a random variable (M11/12SP-IIIa-3)
• illustrates a probability distribution for a discrete random variable and its
properties (M11/12SP-IIIa-4)
Activity 2: Let’s Solve!
Directions: Do what is asked in the following problems.
1. A box contains 12 defective and non-defective batteries. Four batteries are taken
from the box one after the other, and we let N be the number of non-defective
batteries that will be drawn.
a. Determine the sample space.
b. Construct the probability distribution for the random variable N.
2. Suppose you draw 3 handkerchiefs, you have 15 handkerchiefs in your cabinet, 9
of them are blue and 6 of them are yellow. Let Y be the random variable
representing the number of yellow handkerchiefs drawn.
a. Determine the sample space.
b. Construct the probability distribution for the random variable Y.
Name:___________________________________________ Date:____________
Grade/Section: ____________________________________Score:____________
Most Essential Learning Competencies:
• finds the possible values of a random variable (M11/12SP-IIIa-3)
• illustrates a probability distribution for a discrete random variable and its
properties (M11/12SP-IIIa-4)
PERFORMANCE TASK: You Can Do It!
Directions. Using discrete variables, create two different word
problems. Take note that solving the problem requires the
competencies stated above.
*There will be no point if it with the same problem with your
classmate and if it is copied from the internet.
Your output will be graded using this rubric.
4 pts 3 pts 2 pts 1pt
Requirements Student goes Student meets Student hardly Student does
beyond the the requirements meets the not meet the
requirements requirements requirements
Content Appropriate Appropriate Appropriate Appropriate
content is used content is used content may be content is not
for each word for each word used. Student observed.
problem. problem. shows little Student does
Student clearly Student shows understanding not demonstrate
understands some of the an
the understanding of mathematical understanding
mathematical the concepts. of the
concepts. mathematical mathematical
concepts. concepts.
Solution Solution is Solution is Solution is Solution is
correct and all correct, however incorrect; incorrect and
work is shown. there is no work however the student either
shown for the student showed didn’t show
problem. their work and work or worked
made an error the problem
in calculations. incorrectly.
Organization The word The word The word The word
problem is problem is problem is not problem is not
written in clear written in clear written in clear written in clear
and coherent and coherent and coherent and coherent
language. It is language. It is language. It is language, or
easy to follow easy to read easy to follow may not be
and read. most of the time. and read some observed. It is
of the time. difficult to read
and follow.
Mechanics Proper Proper Proper Proper
language, language, language, language,
capitalization capitalization capitalization capitalization
and and punctuation and punctuation and punctuation
punctuation are present with may be used, are not
are present no more than but more than observed.
with no two mistakes. two mistakes.
mistakes.
References:
• Alonzo, George. Statistics and Probability for Senior High School Grade 11.
Makati City: Salinlahi Publishing House, Inc., 2017.
• Belecina, Rene R. Statistics and Probability. Manila: Rex Book Store, 2016.
• POLK School District. “Rubric Writing Math Word Problems.” Retrieved on
February 5, 2021 from
https://www.polk.k12.ga.us/userfiles/313/Two%20step%20word%20pro
blem%20rubric.pdf
