Personalisation of Education by AI and Big Data - Lourdes Guàrdia
Fundamental counting principle PPT LESSON 2
1.
2. REVIEW
Situation
Maria tossed a coin and
wanted a tail
Juan rolls a die and
wants to get numbers
below 4
Experiment
Outcome
Sample Space
Event
Sample space of
event
No. of sample
space of event
𝑻𝒐𝒔𝒔𝒊𝒏𝒈 𝒂 𝒄𝒐𝒊𝒏 𝑹𝒐𝒍𝒍𝒊𝒏𝒈 𝒂 𝒅𝒊𝒆
𝑯𝒆𝒂𝒅 𝒐𝒓 𝑻𝒂𝒊𝒍 𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔
𝒘𝒂𝒏𝒕𝒆𝒅 𝒂 𝒕𝒂𝒊𝒍
𝒈𝒆𝒕𝒕𝒊𝒏𝒈 𝒏𝒖𝒎𝒃𝒆𝒓𝒔
𝒃𝒆𝒍𝒐𝒘 𝟒
𝑺 = {𝑯𝒆𝒂𝒅 , 𝑻𝒂𝒊𝒍} 𝑺 = {𝟏, 𝟐, 𝟑, 𝟒, 𝟓, 𝟔}
𝑺 𝑬𝒗𝒆𝒏𝒕 = {𝟏, 𝟐, 𝟑}
𝑺 𝑬𝒗𝒆𝒏𝒕 = {𝑻𝒂𝒊𝒍}
𝟏 𝟑
3.
4. 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?
CLAUD
E
GRANGE
R
DYROTT
H
CHO
U
CLAUDE AND
DYROTTH
CLAUDE AND
CHOU
GRANGER AND
DYROTTH
GRANGER AND
CHOU
M
A
R
K
S
M
A
N
F
I
G
H
T
E
R
In this experiment, how did we get the number of
possible ways which is 4?
4 ways to choose one marksman and one
fighter
5.
6. Counts the number of
occurrences of an
outcome in an
experiment:
(a) table;
(b) tree diagram;
(c) systematic listing;
and
(d) fundamental counting
OBJECTIV
E
7. 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
METHODS IN COUNTING
POSSIBLE OUTCOMES
8. 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?
EXAMPL
E
Blouse
s
Skirt
9 ways can select her outfit
BY TABLE
9. 9 ways can select her outfit
BY TREE
DIAGRAM
Blouse
s
Skirt
s
12. Flipping a coin and rolling a
die
EXAMPL
E
BY TABLE
Di
e
Coin
12 possible
outcomes
13. BY TREE
DIAGRAM
Flippin
g a
coin
and
rolling
a die
Flipping a
coin
Rolling a die
𝒏 𝑺 = 𝟏𝟐
Outcomes
𝒉𝒆𝒂𝒅, 𝟏
𝒉𝒆𝒂𝒅, 𝟐
𝒉𝒆𝒂𝒅, 𝟑
𝒉𝒆𝒂𝒅, 𝟒
𝒉𝒆𝒂𝒅, 𝟓
𝒉𝒆𝒂𝒅, 𝟔
𝒕𝒂𝒊𝒍, 𝟏
𝒕𝒂𝒊𝒍, 𝟐
𝒕𝒂𝒊𝒍, 𝟑
𝒕𝒂𝒊𝒍, 𝟒
𝒕𝒂𝒊𝒍, 𝟓
𝒕𝒂𝒊𝒍, 𝟔
14. BY SYSTEMATIC
LISTING
Flipping a
coin
Rolling a die
𝒏 𝑺 = 𝟏𝟐
Listing the
Sample space
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
𝐻𝑒𝑎𝑑 𝑜𝑟 𝑇𝑎𝑖𝑙
1,2,3,4,5,6
By combining all possible
outcomes of coin and a die
15. BY FUNDAMENTAL COUNTING
PRINCIPLE
Determine the
possible outcomes
Number of
possible
outcomes
COIN
DIE
HEAD AND TAIL
1,2,3,4,5,6
Count the no. of
possible outcomes
2 possible
outcomes
6 possible
outcomes
2
× 6
12
𝒏 𝑺 = 𝟏𝟐
16. 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
and fundamental counting principle
LET DO
THIS!
BY TREE
DIAGRAM
SUBJE
CT
SCHOOL OUTCOM
E
Scien
ce
Math
U
P
DLS
U
ADMU
U
P
DLS
U
ADMU
𝑺𝒄𝒊𝒆𝒏𝒄𝒆, 𝑼𝑷
𝑺𝒄𝒊𝒆𝒏𝒄𝒆, 𝑫𝑳𝑺𝑼
𝑺𝒄𝒊𝒆𝒏𝒄𝒆, 𝑨𝑫𝑴𝑼
𝑴𝒂𝒕𝒉, 𝑼𝑷
𝑴𝒂𝒕𝒉, 𝑫𝑳𝑺𝑼
𝑴𝒂𝒕𝒉, 𝑨𝑫𝑴𝑼
The University of the Philippines
(UP)
De La Salle
University (DLSU)
Ateneo de Manila University
(ADMU)
BY
FUNDAMENTAL
COUNTING
PRINCIPLE
𝟐 𝒔𝒖𝒃𝒋𝒆𝒄𝒕𝒔 𝟑 𝒔𝒄𝒉𝒐𝒐𝒍𝒔
×
𝟔 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝒄𝒉𝒐𝒊𝒄𝒆𝒔
17. 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
The Punnett
square is a
square diagram
that is used to
predict the
genotypes of a
particular cross
or breeding
experiment.
Blue
eyes
Brown eyes
𝐵
𝑏
𝑏 𝑏
𝑩𝒃 𝑩𝒃
𝒃𝒃 𝒃𝒃
𝟒 𝒑𝒐𝒔𝒔𝒊𝒃𝒍𝒆 𝒄𝒐𝒎𝒃𝒊𝒏𝒂𝒕𝒊𝒐𝒏
18. Fundamental counting
principle
It states that we can find the total number of ways different event
occur by multiplying the number of ways each event can happen.
Other methods in counting possible
outcomes?
BY TABLE
BY TREE
DIAGRAM
BY SYSTEMATIC
LISTING
