MATH 10 QUARTER 3 Week 7

NAME: ______________________________________ GRADE & SECTION: ____________________

Competency

Illustrates the probability of a union of two events (M10SP-IIIg-1).

To the Learners
Before starting the module, I want you to prepare your environment for a healthy learning session and make it free from
any possible disturbances to help you focus with the objectives of this module. Read and follow all the instructions below to
achieve the objectives of this kit. Enjoy and have fun!

1. Read and study all the contents of this module.

2. Follow carefully all the instructions indicated in each section of this module.

3. Perform all the tasks and learning activities in this module.

4. Assess your work using the provided answer key in the module.

5. Enjoy and relax while studying.

Expectations

Lesson 1
Revisiting Probability of Simple and  define simple and compound events.

Compound Events  find the probability of simple and compound events.

 recall and apply the fundamental counting principle.

Lesson 2  illustrate the probability of an event.
Probability of Union of Two Events  illustrate the probability of union of two events.
 explain the general addition rule of probability.
 differentiate the addition rules of probability.

Pre - Test

Direction: Write the letter that corresponds to your answer on your answer sheet.

1. Which of these situations shows a simple event after rolling a fair die?

A. getting 6 C. getting an even number

B. getting an odd number D. getting an odd number greater than two

2. What is the probability of landing a head in a single toss of a fair coin?

1
A. 0 B. C. 1 D. 2
2

3. The probability of union of two events is given by _____ .

A. 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) C. 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)

B. 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) − 𝑃(𝐵) D. 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) − 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)

MATH 10 QUARTER 3 WEEK 7 1

Donnie Boy M. Pineda & Je B. De Venecia Page 1 of 10
4. How many distinct ways can you keep four different books in a book shelf?

A. 4 B. 12 C. 24 D. 120

5. If there are two different pasta dishes, three kinds of sandwiches, and four kinds of drinks available in the menu, how
many different Combo Specials can a customer order?
A. 1 B. 9 C. 12 D. 24

6. It refers to an event that involves two or more simple events.

A. Compound Events B. Exclusive Event C. Mutually Exclusive Event D. Special Event

7. What is the size of the sample space when three distinct fair coins were tossed simultaneously?

A. 2 B. 4 C. 6 D. 8

8. What is the probability of getting a result of three or an even number when you roll a fair die?

2 1 1 1
A. B. C. D.
3 2 3 6

9. Suppose you roll two fair dice simultaneously. What is the probability of getting a double (two of the same number) or
having a sum of ten?

1 1 1 2
A. B. C. D.
12 18 36 9

10. How many elements are there if you draw a face card or a black jack in a standard deck of 52 cards?

A. 1 B. 2 C. 4 D. 12

Looking Back to your Lesson

Direction: Analyze the Venn diagram Figure 1 on the right. Draw a smiling emoji

if the set shows the union or a sad emoji if the set shows the

intersection on the space provided.

1. A ______ B = {3, 6} 4. B ______ C = {6}

2. A ______ B = {1, 2, 3, 5, 6, 7, 8} 5. B ______ C = {2, 3, 4, 6, 8, 9}

3. A ______ C = {1, 3, 4, 5, 6, 7, 9} Figure 1. Venn Diagram of Three

Intersecting Events

Introduction of the Topic

The mathematical theory of probability began with a gambling dispute in 1654 that involves a popular dice game.
Two famous French mathematicians, Blaise Pascal and Pierre de Fermat laid the foundations of probability based on the
interest in gaming and gambling questions of a French noblewoman Antoine Gombaud, Chevalier de Méré (Apostol 1969).

The probability is also used in daily living. If you heard, read, or watched about the weather forecast today and for
the next few days, the PAGASA Weather and Flood Forecasting Center may have used the term possibility, prediction, or
probability in the report.

In the next series of lessons, you will learn some basic concepts and probability formulas for different situations that
you may find helpful for predictions and decision making. If you feel excited and ready, then it’s time to explore, read, and
perform all the activities in the next sections of this module. Have fun!

MATH 10 QUARTER 3 WEEK 7 2

 Lesson 1

REVISITING PROBABILITY OF SIMPLE AND COMPOUND EVENTS

Key Concepts

Probability is a measure of the likelihood of an event to happen.

In calculating probabilities, you will often be asked of the size of the sample space. The size refers to the total number of
outcomes. Hence, on the first example it is two, while on the second example it is six.

What is the probability of a simple event?

The probability of a 𝑷(𝒆𝒗𝒆𝒏𝒕) is equal to the ratio of the number of the favorable (desired) outcomes and the size of
the sample space.
𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐭𝐡𝐞 𝐟𝐚𝐯𝐨𝐫𝐚𝐛𝐥𝐞 (𝐝𝐞𝐬𝐢𝐫𝐞𝐝) 𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬
𝑷(𝒆𝒗𝒆𝒏𝒕) =
𝐬𝐢𝐳𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐩𝐚𝐜𝐞
Since a simple event can only have an exactly one outcome, then, the formula can be simplified to
𝟏
𝑷(𝒔𝒊𝒎𝒑𝒍𝒆 𝒆𝒗𝒆𝒏𝒕) =
𝐬𝐢𝐳𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐩𝐚𝐜𝐞
Example 1

What is the probability of getting a head in a single toss of fair coin?

𝟏
Solution: 𝑃(ℎ𝑒𝑎𝑑𝑠) = Explanation Simple event always has exactly one outcome, while
𝟐
the sample space has a size of two which includes heads and tails.

Example 2 What is the probability of getting a four in a single roll of fair die?

𝟏 Explanation Simple event always has exactly one outcome, while

Solution: 𝑃(𝑓𝑜𝑢𝑟) = the sample space has a size of six which includes one, two, three, four,
𝟔
five, and six.

A spinner is divided into four sections with a pointer at the upper tip. Each section is differently labeled
Example 3
using A, B, C, or D. What is the probability that a single spin will be pointing at section C?

𝟏 Explanation The situation involves equal sections with different labels as

Solution: 𝑃(𝐶) = 𝟒
well, which results to only one outcome for each label, while the sample
space has a size of four which includes A, B, C, and D.

Example 4 What is the probability of getting a number greater than five in a single roll of fair die?

𝟏
Solution: 𝑃(𝑓𝑜𝑢𝑟) = Explanation The situation involves a simple event because there is only
𝟔
one number that is greater than five. You can look at the sample space to
verify such claim: one, two, three, four, five, and six. Yay! you’ve guessed it
right! Six is the only number in the sample space which is greater than five.
While it is obvious that the size of the sample space is also six.

MATH 10 QUARTER 3 WEEK 7 3

 What is the probability of a compound event?
The probability of compound event is equal to the ratio of the number of the favorable (desired) outcomes and
the size of the sample space.
𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐭𝐡𝐞 𝐟𝐚𝐯𝐨𝐫𝐚𝐛𝐥𝐞 (𝐝𝐞𝐬𝐢𝐫𝐞𝐝) 𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬
𝑷(𝒄𝒐𝒎𝒑𝒐𝒖𝒏𝒅 𝒆𝒗𝒆𝒏𝒕) =
𝐬𝐢𝐳𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐩𝐚𝐜𝐞

You may notice that the formula is basically the same with the formula for probability of simple events before it was
simplified. However, since the number of favorable outcomes vary for different situations involving compound events, then,
you cannot simplify this formula.

Example 1 What is the probability of getting a two or five in a roll of fair die? Express your final answer in lowest terms.

𝟐 𝟏
Solution: 𝑃(𝑒𝑣𝑒𝑛) = 𝑜𝑟 Explanation The compound event includes two simple events which
𝟔 𝟑
could be a two or a five. The phrase “two or five” means that a result of two
is acceptable and the result of five is also acceptable. While the sample
space has a size of six which includes one, two, three, four, five, and six.

Example 2 What is the probability of rolling an even number in a fair die? Express your final answer in lowest terms.

𝟑 𝟏 Explanation The compound event includes three simple events which

Solution: 𝑃(𝑒𝑣𝑒𝑛) = 𝑜𝑟
𝟔 𝟐 are the even numbers: two, four, and six. While the sample space has a
size of six which includes one, two, three, four, five, and six.

Example 3 What is the probability of drawing a red face card in a single draw from a standard deck of playing cards?
Express your final answer in lowest terms.

Explanation (Refer to the note below if you are not familiar with the
composition of a standard deck of playing cards.) The compound event
𝟔 𝟑 includes six simple events: the Jack, Queen, and King of diamonds suit
Solution: 𝑃(𝑒𝑣𝑒𝑛) = 𝑜𝑟
𝟓𝟐 𝟐𝟔 and the Jack, Queen, and King of hearts suit. While the sample space
includes all the fifty-two cards in the deck with a size of fifty-two (52).

Note: A standard deck of playing cards contains fifty-two (52) cards. The deck is equally divided
into two colors of twenty-six (26) cards each: black and red. Each color is equally divided into two suits
of thirteen (13) cards each: clubs and spades for black while diamonds and hearts for red. Each suit
contains: Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, and King. The Jack, Queen, and King are also
called the face cards.

Activity 1:
Direction: Solve and write your complete solution on your notebook. Then, exchange your answer on the line for
the word on the left of the question to unlock the hidden message.

𝟏 𝟏 𝟏 𝟏 𝟐 𝟏 𝟏 𝟑
𝟔 𝟑 𝟐 𝟓𝟐 𝟏𝟑 𝟖 𝟒 𝟏𝟎

by Lucius Annaeus Seneca

MATH 10 QUARTER 3 WEEK 7 4

 What is the probability of

A landing a tail in a single toss of fair coin?

IS rolling a multiple of three in a single roll of fair die?

LUCK rolling a number less than two in a single roll of fair die?

MATTER drawing an ace of clubs from a standard deck of playing cards?

MEETING drawing a card of hearts suit from a standard deck of playing cards?

OF drawing an ace or a queen from a standard deck of playing cards?

OPPORTUNITY drawing a red ball from a box containing: two blue balls,

three red balls, and five yellow balls?

PREPARATION spinning yellow from the given wheel Figure 2 Figure 2. Eight Colors Spinning Wheel

Lesson 2

PROBABILITY OF UNION OF TWO EVENTS

Key Concepts

Probability is a measure of the likelihood of an event to happen which is given by

𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐭𝐡𝐞 𝐟𝐚𝐯𝐨𝐫𝐚𝐛𝐥𝐞 (𝐝𝐞𝐬𝐢𝐫𝐞𝐝) 𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬
𝑷(𝒆𝒗𝒆𝒏𝒕) =
𝐬𝐢𝐳𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐩𝐚𝐜𝐞

Fundamental Counting Principle (FCP)

If an event A has m number of outcomes and if for each of these outcomes another event B has n
number of outcomes, then both events together have mn number of outcomes.

Example Suppose you only have three shirts and two pants left in the closet. How many ways can you dress
for today?
Shirts Pants
3 2

3x2=6

You can dress up to six (6) different

ways.

What is the probability of union of two events?

Given any two events A and B, the probability of the union of the events A and B is given by
𝑷(𝑨 ∪ 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) − 𝑷(𝑨 ∩ 𝑩)
which is also referred to as the Addition Rule and sometimes written as
𝑷(𝑨 𝒐𝒓 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) − 𝑷(𝑨 𝒂𝒏𝒅 𝑩)

MATH 10 QUARTER 3 WEEK 7 5

 In the previous module, you have learned that the union of events A and B, denoted as 𝑨 ∪ 𝑩, contains all the
elements of the events A and B. However, the sum of the individual probabilities of A and B, denoted 𝑷(𝑨) + 𝑷(𝑩), double
counts each of the common elements of the events A and B. To illustrate such concept, try to explore the example below

Example 1 What is the probability of rolling a four or an even number in a single roll of a fair die?

Explanation 𝑷൫𝒇𝒐𝒖𝒓൯ 𝑷(𝒆𝒗𝒆𝒏) Explanation

+ The numerator 3
The numerator 1
𝟏 𝟑
counts only the counts all the even
𝟔 𝟔
four on the die numbers two, four,
𝟒
+ and six on the die.
= NOT CORRECT!
𝟔

Figure 3. Computation Showing P(four) + P(even)

Notice 𝑷(𝒇𝒐𝒖𝒓) + 𝑷(𝒆𝒗𝒆𝒏) double counts the four (4), because four is also an even number.

To fix the error in the previous computation, examine the Venn diagram Figure 4.

In the Venn diagram Figure 4, if you let the event A be the four on a die and let B
be the even numbers on a die, you will notice that event A coincides with event B because
four is a common element for both events A and B. You have learned in the previous
Figure 4. Venn Diagram Showing
module that the collection of all the common elements of any two events such as A and B
the Intersection of Four and Even
Numbers on a Die

is called the intersection which is denoted as 𝑨 ∩ 𝑩. Thus, subtracting 𝑃(𝑨 ∩ 𝑩) from 𝑷(𝑨) + 𝑷(𝑩) eliminates the double
counts and gives the correct result.
𝟒 𝟏
Use the sum obtained for 𝑷(𝑨) + 𝑷(𝑩) in Figure 3 which is equal to and subtract the 𝑷(𝑨 ∩ 𝑩) which is you will
𝟔 𝟔
𝟒 𝟏 𝟒−𝟏 𝟑 𝟏
get
𝟔
−𝟔 = 𝟔
= 𝟔
𝑜𝑟 . To phrase the concepts simply, since you only need to count the numbers two,
𝟐

four (not double counting four), and six, then you only have three (3) favorable outcomes divided by the size of your sample
𝟏
space which is six (6). Therefore, is the correct solution.
𝟐

Explore and study more examples!!!

Example 2

What is the probability of drawing a red face card or a diamond from a standard deck of playing cards?

𝑷(𝒓𝒆𝒅 𝒇𝒂𝒄𝒆) + 𝑷(𝒅𝒊𝒂𝒎𝒐𝒏𝒅) − 𝑷(𝒓𝒆𝒅 𝒇𝒂𝒄𝒆 ∩ 𝒅𝒊𝒂𝒎𝒐𝒏𝒅) Note You may apply the
FCP to find the number of
𝟔 𝟏𝟑 𝟑 red face cards.
+ −
Solution 𝟓𝟐 𝟓𝟐 𝟓𝟐 Red Suits × Face Cards
𝟔 + 𝟏𝟑 − 𝟑 𝟏𝟔 𝟒 𝟐 × 𝟑
= 𝒐𝒓
𝟓𝟐 𝟓𝟐 𝟏𝟑
= 𝟔 𝑅𝑒𝑑 𝑓𝑎𝑐𝑒 𝑐𝑎𝑟𝑑𝑠

However, DO NOT apply FCP for finding the intersection because of its restrictive nature UNLESS you
know exactly what you are doing.

The intersection only has the three red face cards of diamonds: Jack, Queen, and King of diamonds.

MATH 10 QUARTER 3 WEEK 7 6

 Example 3 What is the probability of spinning a B or a blue in a single spin using the spinning wheel Figure 5?

There are three B’s: blue There are three blue colors:
Solution
B, orange B, and pink B. two blue A’s and a blue B.

𝑷(𝑩) + 𝑷(𝒃𝒍𝒖𝒆) − 𝑷(𝑩 ∩ 𝒃𝒍𝒖𝒆)

There are The
intersection
eight equal 𝟑 𝟑 𝟏
sections, so + − contains only
𝟖 𝟖 𝟖 one element
the size of the
sample space 𝟑+𝟑−𝟏 𝟓 which is the
Figure 5. Colored Spinning is eight.
= blue B.
𝟖 𝟖
Wheel with Letters

Not all situations that involve probability of union of two (or more) events have common elements. Explore and
study the next example.

Example 4 What is the probability of getting at least two heads when you flip a one-peso, a five-peso, and a ten-
peso coin simultaneously?

The problem involves a compound event consisting of

three simple events. It also involves the union of two events as
indicated by such phrase “at least two heads” for which the coins
show exactly two heads and a head or all the coins show three
heads.

The tree diagram shows the result of flipping each of the

three different coins together with the result of the three coins
flipped simultaneously. The diagram also shows the size of the
sample space which is equal to eight.

Figure 6. Sample Space of Flipping Three Distinct Coins How to count the size of the sample space?

If you do not wish to make a tree diagram or list of the sample space to know its size, then you may apply the
Fundamental Counting Principle.

One Peso Five Peso Ten Peso Result Each coin has two possible outcomes. By multiplying all
2 × 2 × 2 = 8 the numbers corresponding to the total number of

possible outcomes for each coin (𝟐 × 𝟐 × 𝟐) you can get the size of the sample space (8) when all the coins are flipped
simultaneously.
The 𝑷(𝒂𝒕 𝒍𝒆𝒂𝒔𝒕 𝒕𝒘𝒐 𝒉𝒆𝒂𝒅𝒔) means that a result with exactly two heads are allowed as well as the
Solution result with three heads. Hence, you could also write the problem as

𝑷(𝒘𝒊𝒕𝒉 𝒆𝒙𝒂𝒄𝒕𝒍𝒚 𝒕𝒘𝒐 𝒉𝒆𝒂𝒅𝒔) + 𝑷(𝒘𝒊𝒕𝒉 𝒕𝒉𝒓𝒆𝒆 𝒉𝒆𝒂𝒅𝒔)

− 𝑷(𝒘𝒊𝒕𝒉 𝒆𝒙𝒂𝒄𝒕𝒍𝒚 𝒕𝒘𝒐 𝒉𝒆𝒂𝒅𝒔 𝒂𝒏𝒅 𝒘𝒊𝒕𝒉 𝒕𝒉𝒓𝒆𝒆 𝒉𝒆𝒂𝒅𝒔)
𝟑 𝟏
+ − 𝟎
𝟖 𝟖
𝟑+𝟏 𝟒 𝟏 The size of the sample
Solution = 𝒐𝒓
𝟖 𝟖 𝟐 space is eight.

There are three results that There is only one result Notice that there is no common element
show exactly two heads: that shows three heads between the two events (HHT, HTH,
HHT, HTH, and THH. which is HHH. (Refer to THH, and HHH), therefore their
(Refer to Figure 6.) Figure 6.) intersection has a size of zero.

MATH 10 QUARTER 3 WEEK 7 7

 Remember that if the situation involves the probability of the union of two events for which the events have no
common elements the formula can be simplified to

𝑷(𝑨 ∪ 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) − 𝑷(𝑨 ∩ 𝑩)

you will learn more about this kind of probability in your next module. Have fun learning!

Activity 2:

Direction: Solve and write your complete solution on your notebook. Match the picture with an answer provided in the box
below. Then, guess the word that can produce by each pair of pictures.

𝟓 𝟏 𝟒 𝟏 𝟕
𝟏
𝟖 𝟒 𝟏𝟑 𝟐 𝟖

What is the probability of drawing an ace or a spade from a standard deck of playing cards?

What is the probability of drawing a red or a black card from a standard deck of playing cards?

What is the probability of getting a three of a kind (three of the same side of the coin) when you
flip a one-peso, a five-peso, and a ten-peso coins simultaneously?

What is the probability of getting a result with at most two tails when you flip a one-peso, a
five-peso, and a ten-peso coins simultaneously?

Using the spinner in Figure 5, what is the probability of spinning an A or a pink in a single spin?

Using the spinner in Figure 5, what is the probability of spinning a C or a blue in a single spin?

Remember

Probability is a measure of the likelihood of an event to happen which is given by

𝐧𝐮𝐦𝐛𝐞𝐫 𝐨𝐟 𝐟𝐚𝐯𝐨𝐫𝐚𝐛𝐥𝐞 (𝐝𝐞𝐬𝐢𝐫𝐞𝐝) 𝐨𝐮𝐭𝐜𝐨𝐦𝐞𝐬
𝑷(𝒆𝒗𝒆𝒏𝒕) =
𝐬𝐢𝐳𝐞 𝐨𝐟 𝐭𝐡𝐞 𝐬𝐚𝐦𝐩𝐥𝐞 𝐬𝐩𝐚𝐜𝐞

Fundamental Counting Principle (FCP)

If an event A has m number of outcomes and if for each of these outcomes another event B has n number of outcomes,
then both events together have mn number of outcomes.

Addition Rule

The probability of union of events A and B is given by 𝑷(𝑨 ∪ 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) − 𝑷(𝑨 ∩ 𝑩)

Remember that if the situation involves the probability of the union of two events for which the events have no
common elements the formula can be simplified to 𝑷(𝑨 ∪ 𝑩) = 𝑷(𝑨) + 𝑷(𝑩)

MATH 10 QUARTER 3 WEEK 7 8

 Check Your Understanding

I. Direction: Answer each problem involving probability of simple and compound events. Write your complete
solutions on your notebook and encircle/box your final answers. Express your final answers in lowest terms.

Use the Eight Colors Spinning Wheel Figure 2. What is the probability of spinning

1. orange? 2. red or violet? 3. a color other than blue or green?

A deck of twenty-six alphabet cards contains one card for each letter. What is the probability of drawing

4. the letter G? 5. a vowel? 6. the letter M, A, or N?

7. What is the probability of rolling a four in a single roll of a balanced die?

8. What is the probability of rolling an even or odd in a single roll of a fair die?

9. What is the probability of drawing a number card from a standard deck of playing cards?

10. What is the probability of drawing a red spade from a standard deck of playing cards?

II. Direction: Answer each problem involving probability of union of two events. Write your complete solutions on
your notebook and encircle/box your final answers. Express your final answers in lowest terms.

Use the Eight Colors Spinning Wheel Figure 7.

What is the probability of spinning

1. green or one? 2. blue or an even number? 3. orange or an odd number?

4. What is the probability of rolling a sum of six or a sum of seven when you roll two

Figure 7. Colored Spinning

different dice at once?
Wheel with Numbers

5. What is the probability of rolling a sum of eight or a two of a kind when you roll two different dice at once?

6. What is the probability of drawing a face card or a black card in a single draw from a standard deck of playing cards?

7. What is the probability of drawing a red face card or a club in a single draw from a standard deck of playing cards?

8. What is the probability of getting a result with at most one heads or with exactly two tails when you flip three distinct
coins simultaneously?

9. Suppose you simultaneously flipped a coin and rolled a die, what is probability of obtaining a combined result of a
heads and two or a heads and even.

10. Suppose you simultaneously flipped a coin and rolled a die, what is probability of obtaining a combined result of a
heads and three or a tails and odd.

Post-test

Direction: Write the letter that corresponds to your answer on your answer sheet.

1. Which of these situations shows a simple event after rolling a fair die?

A. getting 6 C. getting an even number

MATH 10 QUARTER 3 WEEK 7 9

 B. getting an odd number D. getting an odd number greater than two

2. What is the probability of landing a head in a single toss of a fair coin?

1
A. 0 B. C. 1 D. 2
2

3. The probability of union of two events is given by _____ .

A. 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) C. 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)

B. 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) − 𝑃(𝐵) D. 𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) − 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)

4. How many distinct ways can you keep four different books in a book shelf?

A. 4 B. 12 C. 24 D. 120

5. Assume that you own a “merienda” food stall and you want to offer Busog Combo Specials consisting of a pasta dish,
a sandwich, and a drink. How many unique orders of Busog Combo Specials can you offer if you have these options on the

menu: two pasta dishes, three sandwiches, and four drinks?

A. 1 B. 9 C. 12 D. 24

6. It refers to an event that involves two or more simple events.

A. Compound Events B. Exclusive Event C. Mutually Exclusive Event D. Special Event

7. What is the size of the sample space when three distinct fair coins were tossed simultaneously?

A. 2 B. 4 C. 6 D. 8

8. What is the probability of getting a result of three or an even number when you roll a fair die?

2 1 1 1
A. B. C. D.
3 2 3 6

9. Suppose you roll two fair dice simultaneously. What is the probability of getting a double (two of the same number) or
having a sum of ten?

1 1 1 2
A. B. C. D.
12 18 36 9

10. How many elements are there if you draw a face card or a black jack in a standard deck of 52 cards?

A. 1 B. 2 C. 4 D. 12

Reflection:
Write a journal about your understanding of the lesson on your notebook. Write on your journal about the importance
and how you will be able to use your knowledge of the lesson in real life situations.

I have learned that…

MATH 10 QUARTER 3 WEEK 7 10