REVIEW
Situation
Experiment
Outcome
Sample Space
Event
Sample space of
event
No. of sample
space of event
Maria tossed a coin and
wanted a tail
𝑻𝒐𝒔𝒔𝒊𝒏𝒈 𝒂 𝒄𝒐𝒊𝒏
𝑯𝒆𝒂𝒅 𝒐𝒓 𝑻𝒂𝒊𝒍
𝑺 = {𝑯𝒆𝒂𝒅 , 𝑻𝒂𝒊𝒍}
𝒘𝒂𝒏𝒕𝒆𝒅 𝒂 𝒕𝒂𝒊𝒍
Juan rolls a die and
wants to get numbers
below 4
𝑹𝒐𝒍𝒍𝒊𝒏𝒈 𝒂 𝒅𝒊𝒆
𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔
𝑺 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔}
𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝒏𝒖𝒎𝒃𝒆𝒓𝒔
𝒃𝒆𝒍𝒐𝒘 𝟒
𝑺 𝑬𝒗𝒆𝒏𝒕 = {𝑻𝒂𝒊𝒍}
𝑺 𝑬𝒗𝒆𝒏𝒕 = {𝟏, 𝟐, 𝟑}
𝟏
𝟑
In a tournament of 2 vs 2, you need to
use one fighter and one marksman how
many possible pairs of choosing one
marksman and one fighter?
CLAUDE AND
DYROTTH
CLAUDE AND
CHOU
GRANGER AND
DYROTTH
GRANGER AND
CHOU
4 ways to choose one marksman and one
fighter
In this experiment, how
did we get the number of
possible ways which is 4?
M
A
R
K
S
M
A
N
CLAUD
E
GRANGE
R
DYROTT
H
CHO
U
F
I
G
H
T
E
R
OBJECTIV
E
Counts the number of
occurrences of an
outcome in an
experiment:
(a) table;
(b) tree diagram;
(c) systematic listing;
and
(d) fundamental counting
METHODS IN COUNTING
POSSIBLE OUTCOMES
Table
Use to present the set of all possible outcomes or the sample space of an
experiment.

Tree diagram
An illustration consisting of line segments connecting the starting point up
to the outcome point.

Systematic Listing
Writing down in an organized and systematic way to make sure that none of
the possible outcomes is missed out.

Fundamental Counting Principle
States that we can find the total number of ways different event occur by

EXAMPL
E
Jericho invited Maria to her party: Maria has 3 Blouses (Stripes with ruffles,
long sleeve, and sleeveless) and 3 skirt (red, pink, black) in her closet
reserved for such occasions. Assuming that any skirt can be paired with
any blouse. In how many ways can Maria select her outfit?
BY TABLE
Skirt
Blouse
s
9 ways can select her outfit
BY TREE
DIAGRAM
Blouse
s
Skirt
s
9 ways can select her outfit
BY SYSTEMATIC
LISTING
Blouse
s
Stripes with
ruffles
Long
Sleeve
Sleeveless
Skirt
s
Red
Skirt
Pink
Skirt
Black
Skirt
9 ways can select her outfit
(Stripes with ruffles, Red
skirt)
(Stripes with ruffles, Pink
skirt)
(Stripes with ruffles, Black
skirt)
(Long sleeve, Red
skirt)
(Long-sleeve, Pink
skirt)
(Long-sleeve, Black
skirt)
(Sleeveless, Red
skirt)
(Sleeveless, Pink
skirt)
(Sleeveless, Black
skirt)
BY FUNDAMENTAL COUNTING
PRINCIPLE
Blouse
s
𝟑
Skirt
s
×
9 ways can select her outfit
𝟑
=𝟗
EXAMPL
E
Flipping a coin and rolling a
die
BY TABLE
Coin
Di
e
12 possible
outcomes
Flipping a
coin
BY TREE
DIAGRAM
Rolling a die
Outcomes
𝒉𝒆𝒂𝒅, 𝟏
𝒉𝒆𝒂𝒅, 𝟐
𝒉𝒆𝒂𝒅, 𝟑
Flippin
ga
coin
and
rolling
a die
𝒉𝒆𝒂𝒅, 𝟒
𝒉𝒆𝒂𝒅, 𝟓
𝒉𝒆𝒂𝒅, 𝟔
𝒏 𝑺 = 𝟏𝟐
𝒕𝒂𝒊𝒍, 𝟏
𝒕𝒂𝒊𝒍, 𝟐
𝒕𝒂𝒊𝒍, 𝟑
𝒕𝒂𝒊𝒍, 𝟒
𝒕𝒂𝒊𝒍, 𝟓
𝒕𝒂𝒊𝒍, 𝟔
BY SYSTEMATIC
LISTING
Flipping a
coin
Rolling a die
Listing the
Sample space
𝐻𝑒𝑎𝑑 𝑜𝑟 𝑇𝑎𝑖𝑙
By combining all possible
outcomes of coin and a die
1,2,3,4,5,6
𝑺 = { 𝒉𝒆𝒂𝒅, 𝟏 , 𝒉𝒆𝒂𝒅, 𝟐 , 𝒉𝒆𝒂𝒅, 𝟑 , 𝒉𝒆𝒂𝒅, 𝟒 , 𝒉𝒆𝒂𝒅, 𝟓 , 𝒉𝒆𝒂𝒅, 𝟔 ,
𝒕𝒂𝒊𝒍, 𝟏 , 𝒕𝒂𝒊𝒍, 𝟐 , 𝒕𝒂𝒊𝒍, 𝟑 , 𝒕𝒂𝒊𝒍, 𝟒 . 𝒕𝒂𝒊𝒍, 𝟓 , 𝒕𝒂𝒊𝒍, 𝟔
𝒏 𝑺 = 𝟏𝟐
BY FUNDAMENTAL COUNTING
PRINCIPLE
Determine the
possible outcomes
Count the no. of
possible outcomes
COIN
HEAD AND TAIL
2 possible
outcomes
DIE
1,2,3,4,5,6
6 possible
outcomes
Number of
possible
outcomes
2
×6
12
𝒏 𝑺 = 𝟏𝟐
LET DO
THIS!
SUBJE
CT
Scien
ce
Math
A student is choosing between two subjects Science or Math
and intend to enroll in at UP, DLSU or ADMU. How many
ways can a subject and a school be chosen? By tree diagram
The University
of the Philippines
and fundamental counting
principle
De La Salle
BY TREE
DIAGRAM
SCHOOL
(UP)
University
(DLSU)
Ateneo
de Manila
University
(ADMU)
OUTCOM
E
U
P
DLS
U
ADMU
𝑺𝒄𝒊𝒆𝒏𝒄𝒆, 𝑼𝑷
𝑺𝒄𝒊𝒆𝒏𝒄𝒆, 𝑫𝑳𝑺𝑼
𝑺𝒄𝒊𝒆𝒏𝒄𝒆, 𝑨𝑫𝑴𝑼
U
P
DLS
U
ADMU
𝑴𝒂𝒕𝒉, 𝑼𝑷
𝑴𝒂𝒕𝒉, 𝑫𝑳𝑺𝑼
𝑴𝒂𝒕𝒉, 𝑨𝑫𝑴𝑼
BY
FUNDAMENTAL
COUNTING
PRINCIPLE
𝟐 𝒔𝒖𝒃𝒋𝒆𝒄𝒕𝒔
×
𝟑 𝒔𝒄𝒉𝒐𝒐𝒍𝒔
𝟔 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝒄𝒉𝒐𝒊𝒄𝒆𝒔
LET DO
THIS!
GENETICS: How many possible combinations of blue eyes
and brown eyes can be formed from a mother with (blue eyes)
and a father with (brown eyes)?
bb – BLUE EYES
Bb – BROWN EYES
PUNETTE SQUARE
Blue
eyes
Brown eyes
𝑏
𝑏
𝐵
𝑩𝒃
𝑩𝒃
𝑏
𝒃𝒃
𝒃𝒃
The Punnett
square is a
square diagram
that is used to
predict the
genotypes of a
particular cross
or breeding
experiment.
𝟒 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝒄𝒐𝒎𝒃𝒊𝒏𝒂𝒕𝒊𝒐𝒏
It states that we can find the total number of ways different event
occur by multiplying the number of ways each event can happen.
Fundamental counting
principle
Other methods in counting possible
outcomes?
BY TABLE
BY TREE
DIAGRAM
BY SYSTEMATIC
LISTING