MATHEMATICS10-QUARTER3-MODULE29 (1)LEARN

CO_Q3_Mathematics10 _ Module 29
10
Mathematics
Quarter 3 – Module 29
Introduction to Probability of
Compound Events

Mathematics – Grade 10
Alternative Delivery Mode
Quarter 3 – Module 29 : Introduction to Probability of Compound Events
First Edition, 2020
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10
Mathematics
Quarter 3 – Module 29
Compound Events

Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners,
can continue your studies and learn while at home. Activities, questions,
directions, exercises, and discussions are carefully stated for you to understand
each lesson.
Each SLM is composed of different parts. Each part shall guide you step-by-
step as you discover and understand the lesson prepared for you.
Pre-tests are provided to measure your prior knowledge on lessons in each
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need to ask your facilitator or your teacher’s assistance for better understanding of
the lesson. At the end of each module, you need to answer the post-test to self-
check your learning. Answer keys are provided for each activity and test. We trust
that you will be honest in using these.
In addition to the material in the main text, Notes to the Teacher are also
provided to our facilitators and parents for strategies and reminders on how they
can best help you on your home-based learning.
Please use this module with care. Do not put unnecessary marks on any
part of this SLM. Use a separate sheet of paper in answering the exercises and
tests. And read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering
the tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.

1
What I Need to Know
This module was designed and written with you in mind. It is here to help you
understand the concept of combination.
The scope of this module permits it to be used in many different learning
situations. The lessons are arranged to follow the standard sequence of the course
but the pacing in which you read and comprehend the contents and answer the
exercises in this module will depend on your ability.
After going through this module, you are expected to demonstrate
understanding of key concepts on combination. Specifically, you should be able to:
1) recall the concepts related to sets and probability of simple events,
2) differentiate probability of simple events from compound events,
3) find the probability of the union and the intersection of events,
4) solve problems involving probability of compound events.
What I Know
Let us determine how much you already know about probability of compound
events.
DIRECTION: Read and answer each item carefully. Write only the letter of the
correct answer on your answer sheet.
1) If A = {2, 4, 6, 8, 10, 12, 14, 16} and B = {3, 6, 9, 12, 15}, find n(A ∩ B).
A) 0 B) 2 C) 8 D) 11
2) Which of the following is NOT a true statement?
A) If the probability of an event is closer to 0, then the event is more likely to
happen.
B) The probability that an event will happen is from 0 to 1.
C) The probability of an impossible event is 0.
D) The probability of a certain event is 1.
3) Which of the following is a compound event?
A) Getting at least two heads when tossing a coin thrice.
B) Choosing a female student from a class.
C) Three turning up in rolling die once.
D) Picking a dress in the closet.

2
4) How many possible outcomes are there in tossing three coins once?
A) 3 B) 6 C) 8 D) 12
5) There are 12 apples and 14 oranges in a basket. If a fruit is picked at random
from the basket, what is the probability of picking an orange?
A)
13
7
B)
13
6
C)
12
7
D)
12
6
6) What is the probability that the two children of a couple are both females?
A)
2
1
B)
3
2
C)
5
1
D)
4
1
For items #7 & 8. In an experiment of tossing a six – sided die once, let A be the
event of getting a factor of 6 and B be the event of getting an odd number.
7) What is A ∪ B?
A) {1, 2, 3, 6} B) {1, 2, 3, 5, 6} C) {1, 3, 5} D) {1, 3}
8) What is the cardinality of A ∩ B?
A) 0 B) 1 C) 2 D) 3
9) A box contains 7 black marbles, 8 white marbles, and 5 yellow marbles. If a
marble is drawn at random, what is the probability of getting a black or a
yellow marble?
A)
5
3
B)
4
1
C)
5
2
D)
20
13
10) A letter is randomly chosen from the word “MATHEMATICS”. Find the
probability that a letter A or T is selected.
A)
11
2
B)
11
4
C)
11
6
D)
11
7
11) A die is rolled once. What is the probability that the result is an even
number and a factor of 2?
A)
4
1
B)
3
2
C)
2
1
D)
6
1
12) Two fair dice, each with faces numbered 1 to 6 are rolled once. What is the
probability of getting a sum that is greater than 5 and less than 10?
A)
18
13
B)
6
5
C)
9
5
D)1

3
For items #13 & 14. From a survey of habits, 48% of students interviewed said
that they surf the internet, 36% read pocketbooks, and 28% surf the internet and
read pocketbooks. If a student is chosen from those interviewed, find the
probability that this student
13) surf the internet or read pocketbooks.
A) 72% B) 56% C) 44% D) 16%
14) does NOT surf the internet nor read pocketbooks.
A) 72% B) 56% C) 44% D) 16%
15) In a graduating class of 100 students, 54 will study mathematics, 60 will
study physics, and 35 will study both mathematics and physics. If one of
these students is selected at random, find the probability that the student
will study physics but NOT mathematics.
A)
20
7
B)
5
3
C)
100
21
D)
4
1

4
Lesson
1
Compound Events
When you were in grade 7 and grade 8, you learned the different
mathematics concepts related to sets, Venn diagram and probability of simple
events. These knowledge and skills are very important in understanding the
probability of compound events. Hence, let us review the following concepts and do
the activity that follows.
A) Set is any well-defined collection of objects. The objects comprising the set are
called elements. The notation a ∈ A is used to denote that a is an element of
set A.
1) The number of distinct elements in a set is called the cardinality of the
set. The symbol n(A) represents the number of elements of set A. It is
read as the “number of A” or the “cardinality of set A”.
2) If A and B are any two sets, the intersection of A and B, denoted by
A ∩ B, is the set consisting of all elements that belong to both A and B. In
symbol,
A ∩ B ={ x | x ∈ A and x ∈ B }
This notation is read as “A intersection B is the
set of x such that x is an element of A and x is an
element of B”.
3) The union of two sets A and B, denoted by A ∪ B, is the set of all
elements that belong to A or to B. Symbolically,
A ∪ B ={ x | x ∈ A or x ∈ B }
This notation is read as “A union B is the set of
x such that x is an element of A or x is an
element of B”.
What’s In

5
4) The relationship among sets can be represented using a Venn diagram.
Examples:
Illustrative Example 1. If R is the set of colors in a rainbow and F is the set of
colors in the Philippine flag, a) name the elements of each set and b) their
cardinality. Find the c) union and d) intersection of these two sets.
a) Elements
R = {red, orange, yellow, green, blue, indigo, violet}
F = {blue, red, white, yellow}
b) Cardinality
n(R) = 7
n(F) = 4
c) Union
R ∪ F = { red, orange, yellow, green, blue, indigo, violet, white}
d) Intersection
R ∩ F = { red, yellow, blue}
B) Probability is a measure or estimation of how likely that an event will occur or
happen.
1) The probability of simple event is finding the probability of a single event
occurring.
2) In an experiment with outcomes that are equally likely to happen, the
probability of an event, E, is a ratio that compares the number of
favorable outcomes to the number of possible outcomes. In symbols,
P(E) =
number of favorable outcomes
number of possible outcomes
3) The notation P(E) is read as “the probability of an event E” or simply the
probability of E”.
Illustrative Example 2: A bag has 3 red, 4 yellow, 6 blue and 7 white marbles. If a
marble is picked at random, what is the probability that the picked marble is blue?
Solution:
Total number of marbles in the bag = 20
Number of blue marbles in the bag = 6
A ∪ B A ∩ B
possible outcomes
favorable outcomes

6
P(E) =
number of favorable outcomes
number of possible outcomes
P(blue) =
6
20
=
3
10
C) Other terms associated with probability:
1) Experiments are activities which have well – defined results.
2) Outcomes are possible results of an experiment.
3) Sample Space is the set of all possible outcomes of an experiment.
4) Event is a subset of the sample space.
Illustrative Example 3:
Experiment: Tossing a coin twice.
Outcomes: Getting two heads (HH), getting a head on the first
toss and tail on the second toss (HT), getting tail on
the first toss and head on the second toss (TH) and
getting two tails (TT).
Sample Space: {HT, HH, TH, TT}
Event: Getting at least one head, getting at most one tail, etc
Now, your turn!
Activity 1. Answer what is asked.
1) Name the elements of the following sets:
a) A is the set of Southeast Asia nations.
________________________________________________________________
b) B is the set of months of the year with exactly 30 days.
________________________________________________________________
c) C is the set of positive odd integers less than 10.
________________________________________________________________
2) Find the cardinality of the following sets:
d) D = {positive multiples of 3 less than 30} _____________________
e) E = {positive even prime number} _____________________________
f) F = {distinct letters in the word PHILIPPINES} __________________

7
3) If G = {𝑥/𝑥 𝑖𝑠 𝑎 multiple of 3 between 10 and 28} and
H = {𝑦/𝑦 𝑖𝑠 𝑎 multiple of 6 between 5 and 40}
g) G ∪ H ___________________________
h) G ∩ H ___________________________
4) Linda has 6 roses, 5 anthuriums, 9 daisies, and 10 dahlias in her flower
vase. If she picks one flower at random, what is the probability that she will
pick a
i) rose? ____________________
j) daisy? ____________________
5) Grade 10 - Prestige has 18 male and 24 female students. Suppose that the
officers are chosen at random, what is the probability of choosing a
k) female as the president of this class? _____________________
l) male as the vice-president of this class? _____________________
Let’s have more!
Activity 2. Identify the outcomes, sample space and event of each experiment.
1) Experiment: Rolling a six sided – die once.
Outcomes: _________________________________________________
Sample Space: _________________________________________________
Event: _________________________________________________
2) Experiment: Two leaders are selected from five students A, B, C
D and E to lead a tree planting activity.
Outcomes: _________________________________________________
Sample Space: _________________________________________________
Event: _________________________________________________

8
What’s New
The probability of simple event involves a single event occurring and the
probability of compound events involves more than one event happening
together. Compound events are usually connected by the word “and” or “or”.
Illustrative Example 4.
a) Simple probability: The probability of getting a head when tossing a coin
once.
b) Compound probability: The probability of getting a head and an even
number when tossing a coin once and rolling a die once.
Let us see if you understand simple event and compound events. Do the activity
below.
Activity 3.
Directions: Write S if the required probability is simple and write C if
compound in each of the following items.
_____1) The probability of getting a 4 in rolling a standard die once.
_____2) The probability of choosing a male student for SSG president.
_____3) The probability of getting an even number or a multiple of 3 on a
die in rolling a standard die once.
_____4) The probability of drawing a spade from a standard deck of cards.
_____5) The probability of choosing a male and a Grade10 student for SSG
President.
_____6) The probability of drawing a heart and a red card from a standard
deck of cards.
Always remember the following concept of probability.
𝑃(𝐸) =
𝑛(𝐸)
𝑛(𝑆)
If an event E has n(E) equally likely outcomes and S has n(S) equally
likely outcomes, the probability of event E, is
cardinality of the sample space (all possible outcomes)
cardinality of event E (favorable outcomes)

9
Because the number of favorable outcomes in an event must be less than or
equal to the number of outcomes in the sample space, the probability of any event
E, must be a number from 0 to 1. That is,
0 ≤ P(E) ≤ 1.
Hence, the probability of an impossible event is 0 and the probability of a
certain event is 1.
What is It
Solving the probability of compound events can be illustrated using the
concepts of union and intersection of events and the Venn diagram.
 The union of events A and B, denoted by A ∪ B, is the set of all outcomes in
either A or B.
 The intersection of events A and B, denoted by A ∩ B, is the set of all
outcomes shared by A and B.
Let’s have examples:
Illustrative Example 5. In an experiment of rolling a standard die once and
tossing a coin once, let E denote the event that an even number turns up and let T
denote the event that a tail turns up, respectively. Find the a) union and b)
intersection of these events.
sample space, S = {1H, 2H, 3H, 4H, 5H, 6H, 1T, 2T, 3T, 4T, 5T,6T}
E = {2H, 4H, 6H, 2T, 4T, 6T}
T = {1T, 2T, 3T, 4T, 5T, 6T}
E ∪T = {2H, 4H, 6H,1T, 2T, 3T, 4T, 5T, 6T}
E ∩T = {2T, 4T, 6T}

10
Activity 4. Identify the sample space S, the elements of M, N, M ∪ N and M ∩
N.
1) A family of three children is selected at random from a set of families with
three children each. Let M denote the family that exactly one child is a boy
and N denote the family that exactly two children have the same gender.
a) S = ______________________________________________
b) M = ______________________________________________
c) N = ______________________________________________
d) M ∪ N = __________________________________________
e) M ∩ N = __________________________________________
2) In an experiment of turning a spinner as shown at the
right, let M denote the event that the arrow will stop on
an odd number and N denote the event that the arrow
will stop on numbers less than 6.
a) S = __________________________________________
b) M = _________________________________________
c) N = ______________________________________________
d) M ∪ N = __________________________________________
e) M ∩ N = __________________________________________
This time, let’s have examples on solving probability of compound events.
Example 1. A six-face die which contains numbers of dots from 1 to 6 is rolled
once. Find the probability of getting an:
a) even number or a multiple of 3.
b) even number and a multiple of 3.
Solution:
The experiment is rolling a die once, whose sample space, S, is
S = {1, 2, 3, 4, 5, 6}
n(S) = 6 cardinality of the sample space
The elements of the two events are:
A = {2, 4, 6} Let A be the event of getting an even number.
B = {3, 6} Let B be the event of getting a multiple of 3.
a) Solve for P(A ∪ B) since problem a illustrates union of two events.
A ∪ B = {2, 3, 4, 6} union of A and B
n (A ∪ B) = 4 number of favorable outcomes n(E)
P(A ∪ B) =
n(A∪B)
n(S)
P(A ∪ B) =
4
6
=
2
3
∴The probability of getting an even number or a multiple of 3 is .
3
2
4
6
7
3
2
1
5
8
In 𝑃(𝐸) =
𝑛(𝐸)
𝑛(𝑆)
, let n(E) = n(A∪B)
Substitute n(A∪B) by 4 and n(S) 𝑏𝑦 6

11
b) Solve for P(A ∩ B) since problem b illustrates intersection of two events.
A ∩ B = {6} intersection of A and B
n(A ∩ B) = 1 number of favorable outcomes n(E)
P(A ∩ B) =
n(A ∩ B)
n(S)
P(A ∩ B) =
1
6
∴The probability of getting a result that is both an even number and a
multiple
of 3 is .
6
1
Example 2.
Two fair dice are rolled once. Find the probability that both dice turn up
a) the same number or that the sum of the numbers is less than 7.
b) the same number and that the sum of the numbers is less than 7.
Solution:
The experiment is rolling two dice once, whose sample space, S, is
S = {(1,1), (1,2),…, (3,1), (3,2),…, (6,4), (6,5), (6,6)}
n(S) = 36
Let the two events that are involved be:
C = the event that both dice turn up the same number.
D = the event that the sum of the numbers is less than 7.
The elements of the two events are
C = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)}
D = {(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1),
(3,2), (3,3), (4,1), (4,2), (5,1)}
a) Solve for P(C ∪ D) since problem a illustrates union of two events.
C ∪ D = {(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4),
(3,1), (3,2), (3,3), (4,1), (4,2), (4,4), (5,1), (5,5), (6,6)}
n(C ∪ D) = 18
P(C ∪ D) =
n(C ∪ D)
n(S)
=
18
36
=
1
2
In 𝑃(𝐸) =
𝑛(𝐸)
𝑛(𝑆)
, let n(E) = n(A∩B)
Substitute n(A∩B) by 1 and n(S) 𝑏𝑦 6
∴The probability of both dice turn up the same number or that the sum
of the numbers is less than 7 is .
2
1

12
b) Solve for P(C ∩ D) since problem b illustrates intersection of two events.
C ∩ D = {(1,1), (2,2), (3,3)}
n (C ∩ D) = 3
P(C ∩ D) =
n(C ∩ D)
n(S)
=
3
36
=
1
12
∴The probability of both dice turn up the same number and that the sum of
the numbers is less than 7 is .
12
1
Example 3. Three coins are tossed. Find the probability of getting at least one
head.
Solution:
The experiment is tossing three coins, whose sample space, S, is
S = {HHH,HHT, HTH, HTT, TTT, TTH, THT, THH}
n(S) = 8
The event is to get at least one head, which has three possible cases- either
the favorable outcomes should have 1 head or 2 heads or 3 heads.
A = {HTT, TTH, THT} Let A be the event that one head turns up
B = {HHT, HTH, THH} Let B be the event that two heads turn up
C = {HHH} Let C be the event that three heads turn up
A ∪ B ∪ C = {HTT, TTH, THT, HHT, HTH, THH, HHH}
n(A ∪ B ∪ C) = 7
Hence,
P(at least one head) = P(A ∪ B ∪ C)
P(A ∪ B ∪ C) =
n(A ∪ B ∪ C)
n(S)
=
7
8
∴ The probability of getting at least one head in tossing 3 coins is
8
7
.

13
Example 4. The Venn Diagram at the right
shows the probabilities of Grade 10 students
who joined either Mathematics Club (M) or
Science Club (S).
a) Find the probability of selecting a student
who joined Mathematics Club or Science Club.
b) Find the probability of selecting a student who joined Mathematics and Science
Club.
Solution: The diagram represents the total sample space of the two events M
and S because the sum of all the values in the diagram is
0.43 + 0.12 + 0.38 + 0.07 = 1.
a) One way to solve the probability of M ∪S is to add all the probabilities
found within the two circles in the diagram. Thus,
P(M ∪ S) = 0.43 + 0.12 + 0.38 = 0.93
b) The probability of M ∩S is the value in the overlapping region 0.12.
Example 5.A poll conducted by the school canteen showed that 45 students liked
hamburger (H), 60 students liked egg sandwich (E), 27 liked both hamburger and
egg sandwich and, 12 liked neither snacks. What is the probability of selecting a
student who likes hamburger or egg sandwich?
Solution:
Illustrate the problem using Venn diagram so that we can visualize the
probabilities easier.
 Because 27 is the number of students who liked both hamburger and egg
sandwich, we place 27 in the intersection of the two sets.
 There are 45 students who liked hamburger but 27 were already placed
inside circle H. Hence, there are 45 – 27 = 18 students who liked hamburger
only.
 There are 60 students who liked egg sandwich but 27 were already placed
inside circle E. Hence, there are 60 – 27 = 33 students who liked egg
sandwich only.
M S
0.43 0.38
0.12
0.07
H E
18 33
27
12

14
 12 students neither liked hamburger nor egg sandwich so it will be placed
outside the two circles.
 Thus the number of elements in the sample space, S, is
18 + 27 + 33 + 12 = 90.
 To solve for the probability of selecting a student who liked hamburger or egg
sandwich is to solve for P(H ∪ E).
P(H ∪ E) =
n(H ∪ E)
n(S)
P(H ∪ E) =
18 + 27 + 33
90
P(H ∪ E) =
78
90
=
13
15
∴The probability of selecting a student who like hamburger or egg sandwich is
15
13
.
Example 6.
Out of 250 tourists, 146 visited Korea (K), 108 visited Japan (J), 142 visited Hong
Kong (H), 70 visited Korea and Japan, 71 visited Japan and Hong Kong, 82 visited
Korea and Hong Kong and 46 visited Korea, Japan and Hong Kong.
Solution:
The total number of elements in the sample space, S, is
n(S) = 40 + 24 + 13 + 36 + 46 + 25 + 35 + 31 = 250
a) P(K) =
n(K)
n(S)
=
40 + 24 + 36 + 46
250
=
146
250
=
73
125
b) P(only K) =
n(only K)
n(S)
=
40
250
=
4
25
25
31
K
46
24
36
35
40
13
J
H
The Venn diagram at the right
illustrates the relationship of these
sets of data. If a tourist is
randomly chosen from this group,
what is the probability of choosing
a tourist who visited
a) Korea?
b) Korea only?
c) Japan or Hong Kong?
d) Korea and Hong Kong?
e) Hong Kong but not Japan?

15
c) P(J ∪ H) =
n(J ∪ H)
n(S)
=
24 + 13 + 46 + 25 + 36 + 35
250
=
179
250
d) P(K ∩ H) =
n(K ∩ H)
n(S)
=
46 + 36
250
=
82
250
=
41
125
f) P(H but not J) =
n(H but not J)
n(S)
=
36+35
250
=
71
250
What’s More
Now, your turn.
Activity 5.
What is the mathematical term for the division sign (÷)?
1
2
15
1
2
1
15
0
8
15
Directions: To answer the question above, solve the following problem by
answering the items that follow. Then, match your answer to the decoder.
Problem: Number cards 1 through 30 are shuffled and placed on the table face
down. One card is chosen at random. What is the probability that the number
chosen is:
E) a multiple of 3 or a multiple of 4?
L) a multiple of 3 and a multiple of 4?
O) an even number or an odd number?
U) an even number and an odd number?
S) a multiple of 5 or contains the digit 2?
B) a multiple of 3 and contains the digit 2?
Activity 6. Out of the 250 Grade 10 students, 120 liked mathematics (M), 160
liked science (S) and 75 liked both mathematics and science.
a) Draw a Venn diagram illustrating this problem.
If a student is selected from this group, what is the probability that
b) he/she liked mathematics or science?
c) he/she did NOT like any of the two subjects?

16
Activity 7.
What do you call the division slash (/)?
9
50
7
20
21
100
17
25
63
100
1
10
3
50
Directions: To answer the question above, solve the following problem by
answering the items that follow. Then, match your answer to the decoder.
Problem. Out of 500 surveyed students, 225 liked pop music, 215 liked rock
music, 175 liked country music, 90 liked pop and country music, 125 liked pop
and rock music, 110 liked rock and country music and 50 liked pop, rock, and
country music.
The Venn diagram below shows the relationship of these sets of data.
If a student is selected at random from this group, what is the probability of
choosing a student who liked
I) country music?
E) rock music only?
V) pop and country music?
U) pop or rock music?
R) rock but not country?
G) pop or rock or country music?
L) pop and rock and country music?
60
160
Pop
50
75
40
25
60
30
Rock
Country

17
Let us summarize what we have learned in our discussion.
Activity 8. Fill in the blanks with words that will best complete the statements
given below. Choose your answer from the answer box below
 1 are set of repeated activities which have well-defined results
and 2 are the possible results of these activities.
 3 is the set of all possible outcomes of an experiment and any
of its subset is called a/an 4 .
 In an experiment with equally probable outcome, to determine the
probability of an event E, you can use the formula
)
(
)
(
)
(
S
n
E
n
E
P  , where n(E) is
the number of 5 outcomes and n(S) is the number of 6
outcomes.
 If P(E) = 0, then E is a/an 7 event, and if P(E) = 1, then E is
a/an 8 event.
 The 9 of two events is the set of all outcomes that are in at least
one of the event while the 10 of two events is the set of all
outcomes that are in both events.
Answer Box
Probability Intersection Impossible Outcome
Certain Experiment Cardinality Possible
Event Favorable Union Sample Space
Reflect!
1. I’m doing well with __________________________________________________.
2. I still need help with_________________________________________________.
3. I commonly made mistake in ________________________________________.
What I Have Learned

18
What I Can Do
Let us solve more problems on compound probability!
Activity 9. Solve the following problems:
1) Out of the 45 books in the bookshelves, 18 are mathematics books, 10 are
science books, 9 are history books and 8 are story books. If you pick one
book at random, what is the probability that it is a science or mathematics
book?
2) In a particular class, 78% of the students have a smartphone, 38% have a
smartphone and a tablet, and 3 % have neither a smartphone nor a tablet.
Find the probability that a randomly selected student has a
a) tablet?
b) tablet or a smartphone?
c) smartphone but does not have a tablet?
3) In a junior high school completing class of 510 students, 110 are on the
Science, Technology and Engineering (STE) Program. Of these, 78 of the STE
Program students and 112 of the non-STE program students will take STEM
as their senior high school track. A student is selected from the class, what
is the probability that the student chosen will:
a) take STEM as their senior high school track?
b) not take STEM and on the Science, Technology and Engineering
Program?
c) take STEM or on the Science, Technology and Engineering Program?
4) A sample survey results of the talents of some grade 10 students are given in
the following table.
Dancing Singing Total
Male 28 24
Female 32 26
Total
If a student is selected at random from this group, what is the probability
that the student selected is a
a) male?
b) female whose talent is singing?
c) student whose talent is dancing?
d) male whose talent is singing?

19
Assessment
Let us determine how much you have learned from this module.
DIRECTIONS: Read and answer each item carefully. Write only the letter of the
correct answer on your answer sheet.
1) If A = {2, 4, 6, 8, 10, 12, 14, 16} and B = {3, 6, 9, 12, 15}, find n(A ∪ B).
A) 0 B) 2 C) 8 D) 11
2) Which of the following is a true statement?
A) The probability of a certain event is 0.
B) The probability that an event will happen is from 0 to 1.
C) The closer is the probability of an event to 0, the more likely it is to
happen.
D) In an experiment with outcome that are equally likely to happen, the
probability of an event is the ratio that compares the number of favorable
outcomes to the number of not favorable outcomes.
3) Which of the following does NOT illustrate compound events?
A) Getting a 4 or an even number in rolling a standard die.
B) Choosing a female and a grade 10 student.
C) Picking a blue or a pink dress in the closet.
D) Head turning up in tossing a coin once.
4) How many possible outcomes are there in tossing a coin once and rolling a die
once?
A) 3 B) 6 C) 8 D) 12
5) There are 22 apples and 24 oranges in a basket. If a fruit is picked at random,
what is the probability of picking an apple?
A)
23
12
B)
23
11
C)
22
11
D)
11
6
6) Find the probability of getting at least 2 heads in tossing a coin thrice?
A)
2
1
B)
3
2
C)
5
1
D)
4
1
For items 7 & 8. In tossing a six – sided die, let A be the event of getting a factor of
4 and B be the event of getting an even number.
7) What is A ∩ B?
A) {1, 2, 4} B) {2, 4, 6} C) {2,4} D) {1, 2, 4, 6}

20
8) What is the cardinality of A ∪ B?
A) 4 B) 3 C) 2 D) 1
9) A box contains 8 black marbles, 12 white marbles, and 5 yellow marbles. If a
marble is drawn at random, what is the probability of getting a black or a
white marble?
A)
25
17
B)
25
12
C)
25
13
D)
5
4
10) Find the probability of choosing the letter M or the letter E from the word
“MATHEMATICS”.
A)
11
3
B)
11
4
C)
11
5
D)
11
6
11) A die is rolled once. What is the probability of getting a result which is an
odd number and a factor of 6?
A)
2
1
B)
3
1
C)
3
2
D)
6
1
12) Two fair dice are rolled once. What is the probability of getting a sum that is
greater than 6 but less than 9?
A)
18
5
B)
3
2
C)
18
7
D)
36
11
For items 13 & 14. From a survey of habits, 52% of students interviewed said that
they surf the internet, 28% read pocketbooks, and 15% surf the internet and read
pocketbooks. If a student is chosen from those who were interviewed, find the
probability that this student
13) surf the internet or read pocketbooks.
A) 80% B) 67% C) 65% D) 15%
14) does NOT surf the internet nor read pocketbooks.
A) 15% B) 35% C) 65% D) 85%
15) In a graduating class of 100 students, 65 will study mathematics, 70 will
study physics, and 40 will study both mathematics and physics. If one of
these students is selected at random, find the probability that the student
will study physics but NOT mathematics.
A)
10
3
B)
20
9
C)
20
1
D)
4
1

21
This time, let’s have more challenging problems to solve!
Activity 10. Answer the following problems:
1) An experiment involves rolling a die and flipping a coin once if even number
turns up and flipping a coin twice if odd number turns up on the die. Let A
be the event that the result of the die is a number less than 3; let B be the
event that 2 tails occur.
a) List the elements of the sample space, S.
b) List the elements of event A.
c) List the elements of event B.
d) What is the probability of A ∪ B?
e) What is the probability of A ∩ B?
2) Of the 300 grade 10 students of a certain high school, 120 joined
Mathematics club, 115 joined Science club and 100 joined English club.
Furthermore, 55 joined Mathematics and Science club, 50 joined
Mathematics and English club and 40 joined Science and English club.
Finally, 80 students did not join any of these clubs. If a student is selected
from this group, find the probability that the chosen student joined
a) all the three clubs.
b) Mathematics or the English club.
c) any of the three clubs.
d) Science club only.
e) Mathematics and Science club but not English club.
Additional Activities

22
What
I
Know
1)
B
4)
C
7)
B
10)
B
13)
B
2)
A
5)
A
8)
C
11)
D
14)
C
3)
A
6)
D
9)
A
12)
C
15)
D
Activity
1
a)
A
=
{Philippines,
Thailand,
Singapore,
f)
n(F)
=
7
Malaysia,
Cambodia,
Vietnam,
Laos
g)
G
∪
H
=
{6,
12,
15,
18,
21,
24,
27,
30,
36}
Timor
Leste,
Myanmar,
Brunei,
Indonesia}
h)
G
∩
H
=
{12,
18,
24}
b)
B
=
{April,
June,
September,
November
}
i)
P(rose)
=
1
5
c)
C
=
{1,
3,
5,
7,
9}
j)
P(daisy)
=
3
10
d)
n(D)
=
9
k)
P(female)
=
4
7
e)
n(E)
=
1
l)
P(male)
=
3
7
Activity
3
1)
S
2)
S
3)
C
4)
S
5)
C
6)
C
Activity
2
1)
Outcomes:
Rolling
a
one,
a
two,
a
three,
a
four,
a
five
and
a
six.
Sample
Space:
{1,
2,
3,
4,
5,
6}
Event:
Rolling
an
even
number,
rolling
an
odd
number,
etc.
2)
Outcomes:
Selecting
A
&
B,
B
&
C,
C
&
D,
D
&
E,
E
&A,
B
&
D,
B
&
E,
C
&
E,
A
&
C,
D
&
A
Sample
Space:
{AB,
BC,
CD,
DE,
AE,
BD,
BE,
CE,
AC,
DA}
Event:
A
must
be
one
of
the
two.
C
must
not
be
selected,
etc.
Activity
4
1)
S
=
{BBB,
BBG,
BGB,
BGG,
GGG,
GGB,
GBG,
GBB}
2)
S
=
{1,
2,
3,
4,
5,
6,
7,
8}
M
=
{BGG,
GGB,
GBG}
M
=
{1,
3,
5,
7}
N
=
{BBG,
BGB,
BGG,
GGB,
GBG,
GBB}
N
=
{1,
2,
3,
4,
5}
M
∪
N
=
{BBG,
BGB,
BGG,
GGB,
GBG,
GBB}
M
∪
N
=
{1,
2,
3,
4,
5,
7}
M
∩
N
=
{BGG,
GGB,
GBG}
M
∩
N
=
{1,
3,
5}
Activity
5
OBELUS
Activity
6
a)
b)
𝑃(𝑀
∪
𝑆)
=
41
50
c)
𝑃(𝑛𝑜𝑡
𝑀
∪
𝑆)
=
9
50
Activity
7
VIRGULE
Activity
8
1)
Experiment
3)
Sample
space
5)
favorable
7)
impossible
9)
union
2)
outcomes
4)
event
6)
possible
8)
certain
10)
intersection
Activity
9
1)
28
45
2)
a)
57%
b)
97%
c)
40%
3)
a)
19
51
b)
16
255
c)
37
85
4)
a)
26
55
b)
13
55
c)
6
11
d)
12
55
Activity
10
1)
a)
𝑆
=
{2𝐻,
2𝑇,
4𝐻,
4𝑇,
6𝐻,
6𝑇,
1𝐻𝐻,
1𝐻𝑇,
1𝑇𝐻,
1𝑇𝑇,
3𝐻𝐻,
3𝐻𝑇,
3𝑇𝐻,
3𝑇𝑇,
5𝐻𝐻,
5𝐻𝑇,
5𝑇𝐻,
5𝑇𝑇}
b)
𝐴
=
{1𝐻𝐻,
1𝐻𝑇,
1𝑇𝐻,
1𝑇𝑇,
2𝐻,
2𝑇}
c)
𝐵
=
{1𝑇𝑇,
3𝑇𝑇,
5𝑇𝑇}
d)
𝑃(𝐴
∪
𝐵)
=
4
9
e)
𝑃(𝐴
∩
𝐵)
=
1
18
2)
a)
1
10
b)
17
30
c)
11
15
d)
1
6
e)
1
12
Assessment
1)
D
4)
D
7)
C
10)
A
13)
C
2)
B
5)
B
8)
A
11)
B
14)
B
3)
D
6)
A
9)
D
12)
D
15)
A
Answer Key
75
M
S
45
85
45

23
References:
Judith A. Beecher, Algebra and Trigonometry. (Addison Wesley,2007).
R. Larson, Precalculus with Limits. (Belmont, CA: Brooks/Cole,Cengage
Learning,2011).
Rod Pierce, - "Introduction to Sets” Math Is Fun (2020),accessed
http://www.mathisfun.com
Christophere Stover and Eric W.Weisstein, "Set", MathWorld-A Wolfram, accessed
2020, https:// mathworl.wolfram.com/set.html
“Compound Events,” SlideShare,accessed 2020, https://slideshare.net
“Probability of Simple Compound, and Complementary events”, Study.com,
accessed 2020, https://www.study.com

For inquiries or feedback, please write or call:
Department of Education - Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex
Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph

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