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Two sports who were participated by grade 10-students last intramurals are shown in the Venn diagram below. Questions: ______ 1. How many students are in grade ...
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Department of Education
Quarter 3 – Week 6:
Probability of a Union of Two Events
Z est for P rogress Z eal of P artnership
Name of Learner: ___________________________
Grade & Section: ___________________________
Name of School: ___________________________
What I Need to Know
The module contains only one lesson: Lesson 7 – Illustrates the probability of a union of two events
In this module, you are expected to:
What I Know
Directions. Choose the letter of the correct answer. Write the letter of your answer on the space provided.
_____1. What do we call the results on an experiment?
A. Outcomes B. Probability C. Event D. Sample
_____ 2. What refers to the like hood for something to happen.
A. Outcomes B. Probability C. Event D. sample
______3. What do you call an event consist of more than one outcome?
A. Outcomes B. Probability C. Compound D. Simple
______4. Which is not a sample space of a die?
A. 1 B. 4 C. 6 D. 7
_____ 5. What refers to a subset of the sample space?
A. outcome B. experiment C. event D. result
_____ 6. Which is not an example of simple event?
A. Flipping a coin C. Rolling a die B. Flipping a coin and a die D. Picking a card from a deck
_____ 7. When the probability is 1, then an event is ________ to happen?
A. certain B. impossible C. even chance D. likely
_____8. When the probability is 0.75, then an event is _______ to happen?
A. certain B. impossible C. even chance D. likely
_____ 9. What type of event is “tossing a coin”?
A. simple B. compound C. result D. sample space
_____10. What refers to something which will never to happen?
a. certain b. impossible c. even chance d. likely
What is it
Diagram 1. Diagram 2.
From the above activity, you were able to recognize that the events in the given
situation are not simple events. This is because in finding the sample, you need to
find first the sample space using the fundamental counting principle. The events
mentioned here are called compound events. Typically, when the sample space is
finite, any subset of the sample space is an event. Any subset of the sample space is
an event.
Compound Events: Events which consist of more than one outcome are called
compound events. A compound event consists of two or more simple events.
Union of two events:
In Diagram 1, If two events, A and B don’t have an intersection, 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)
In Diagram 2, If two events, A and B have an intersection, 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)
The union of two events is the set that contains all elements that are in at
Union is denoted by the word “or” and symbol Ս. Intersection is denoted by the word “and” symbol ∩.
To illustrate the union of two events, it is often useful to use Venn diagram to visualize the probabilities. Just look the two diagrams below.
Example 1: A small eatery serves lunch for all. A set of menu consists of 1 type of rice and 1 type of dish. The tree diagram below shows the possible menu combinations_._
Questions:
Example 2: Roll a coin and a die simultaneously. The table below shows the possible result of the experiment.
Questions:
1 2 3 4 5 6
H H1 H2 H3 H4 H5 H
T T1 T2 T3 T4 T5 T
What’s More
Activity 3A. Count me up!
Two sports who were participated by grade 10-students last intramurals are shown in the Venn diagram below.
Questions:
__________ 1. How many students are in grade 10 class?
__________ 2. How many students participated in basketball?
__________ 3. How many students participated in volleyball?
__________ 4. How many students participated in both basketball and volleyball?
__________ 5. How many students participated in basketball or volleyball sports?
Activity 3B. Let us roll it!
You are task to toss 2 dice at the same time.
________1. How many possible outcomes in getting 2 and 3?
________2. How many possible outcomes in getting 5 and 3?
________3. How many possible outcomes in getting both even numbers?
________4. How many possible outcomes in having 1 or 5?
________5. How many possible outcomes in having both odd numbers?
18
Basketball
Volleyball
Activity 3C. Toss and Tally…
Rodrigo wants to toss a coin and a icosahedron which has congruent faces numbered 1 to 20 at the same time. Answer the table and all questions that follow below.
Questions:
What I Have Learned
Activity 4. Matching Me Now! Directions: Match Column A from Column B. Choose the letter of the correct answer on the space provided.
A B.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
H
T
_____1. It is denoted by the word “or”.
_____2. How many possible outcomes if you toss two dice?
_____ 3. It consists of two or more events
_____4. How many possible outcomes if you flip two coins?
_____ 5. It is the result of an experiment.
A. Outcome
B. 36
C. Union
D. Compound
E. 4
F. Intersection
Assessment
Directions: Choose the letter of the correct answer. Write your answer on the space
provided.
______1. What do you call an event consists of two or more simple events. A. Compound B. Simple C. Probability D. Outcome
______2. What is the symbol used for Union?
A. U B. ∩ C. u D. U’ ______3. What is the symbol used for intersection? A. U B. ∩ C. Ս D. U’
For items 4-6.
_____4. How many possible outcomes are there?
A. 8 B. 10 C. 12 D. 14
_____5. How many possible outcomes are there selecting orange?
A. 2 B. 4 C. 6 D. 8
_____6. How many possible outcomes are there selecting sisig or lemon?
A. 4 B. 6 C. 8 D. 10
_____7. How many possible outcomes if you roll 2 dice?
A. 6 B. 12 C. 24 D. 36
_____8. How many possible outcomes if you toss a coin and a die?
A. 6 B. 8 C. 10 D. 12
For items 9-10.
3
_____9. How many samples are there?
A. 8 B. 12 C. 16 D. 24
_____10. How many samples are in A or B?
A. 9 B. 11 C. 13 D. 15
Additional Activity
Activity 6: Report it to me!
A. In a local clinic, do a research to determine the number of child births for each month last year.
B. In your school, determine the number of absentees in a class per month school year.
Use basic concept of union of events to come up with a report showing the number of the occurrences.
The report should contain the following:
a. Representation of collected data in a table b. Process of the data gathering c. Illustrate the collected data on a Venn diagram.
Criteria 4 3 2 1
Representation of Data and Explanation
It is complete, organized and clear
It is complete and organized
It is complete but disorganized
It is incomplete and disorganized
Process Has correct and appropriate illustration
Has correct illustration with minor errors
Has illustration with major errors
Has no illustration
Activity 3C:
Adobo Fried Rice Sisig
Bulalo
Adobo Steamed Rice Sisig
Bulalo
Assessment:
Development Team
Writer: Mark Jayson T. Dimain Monching National High School
Editor/QA: Ivy V. Deiparine Pede I. Casing
Reviewer: Gina I. Lihao EPS – Mathematics
Illustrator: Layout Artist: Management Team: Evelyn F. Importante OIC- CID Chief EPS
Dr. Jerry C. Bokingkito OIC- Assistant SDS
Dr. Aurilio A. Santisas, CESE OIC- Assistant SDS
Dr. Jeanelyn A. Aleman, CESO VI OIC-Schools Division Superintendent
References
Callanta, Melvin M.,Allan M. Canonigo, Arnaldo I. Chua, Jerry D. Cruz, et.al,
2015,
Mathematics Learner’s Module – Grade 10, edited by Maxima J. Acelajado, 5 th^ floor Mabini Building, Deped Complex Meralco Avenue, Pasig City, Rex Books Store, Inc.
Bryant, Merden L., Leonides E. Bulalayao, Melvin M. Callenta, Jerry D. Cruz, et.al,
2014, Mathematics Learners’s Material – Grade 9 , edited by Debbie Marie B. Versoza, PhD, 5th^ floor Mabini Building, Deped Complex Meralco Avenue, Pasig City, Phillipines 1600
