SlideShare a Scribd company logo
1 of 30
Introduction to Counting and Probability

Some Terms
“Probability

is the branch of mathematics that
provide quantitative description of the likely
occurrence of an event.
Outcome – any possible result of an experiment or
operation
Sample space – the complete list of all possible
outcomes of an experiment or operation
Event – refers to any subset of a sample space
Counting – operation used to find the number of
possible outcomes
Introduction to Counting and Probability

Counting Problems
Counting problems are of the following kind:
“How

many combinations can I make with 5 Tshirts, 4 pairs of pants, and 3 kinds of shoes?
“How many ways are there to pick starting 5
players out of a 12-player basketball team?”
Most importantly, counting is the basis for
computing probabilities.
Example;:“What is the probability of winning the
lotto?”
Introduction to Counting and Probability

Counting Problems
Example:
Ang Carinderia ni Jay ay may breakfast promo
kung saan maaari kang makabuo ng combo meal
mula sa mga sumusunod:
SILOG

DRINKS

DESSERT

TAPSILOG

KAPE

SAGING

TOSILOG

MILO

BROWNIES

LONGSILOG

ICED TEA

BANGSILOG
Introduction to Counting and Probability

Counting Problems
Example:
Question: If you want to create a combo meal
by choose one of each kind, how many choices
can you have?
SILOG

DRINKS

DESSERT

TAPSILOG

KAPE

SAGING

TOSILOG

MILO

BROWNIES

LONGSILOG

ICED TEA

BANGSILOG
Introduction to Counting and Probability

Counting Problems
SILOG

DRINKS

DESSERT

TAPSILOG

KAPE

SAGING

TOSILOG

MILO

BROWNIES

LONGSILOG

ICED TEA

BANGSILOG

KAPE
TAPSILOG

SAGING
BROWNIES

MILO

SAGING
BROWNIES

ICED TEA

SAGING
BROWNIES
Introduction to Counting and Probability

Counting Problems
SILOG

DRINKS

DESSERT

TAPSILOG

KAPE

SAGING

TOSILOG

MILO

BROWNIES

LONGSILOG

ICED TEA

BANGSILOG

KAPE
TOSILOG

SAGING
BROWNIES

MILO

SAGING
BROWNIES

ICED TEA

SAGING
BROWNIES
Introduction to Counting and Probability

Counting Problems
SILOG

DRINKS

DESSERT

TAPSILOG

KAPE

SAGING

TOSILOG

MILO

BROWNIES

LONGSILOG

ICED TEA

BANGSILOG

KAPE
LONGSILOG

SAGING
BROWNIES

MILO

SAGING
BROWNIES

ICED TEA

SAGING
BROWNIES
Introduction to Counting and Probability

Counting Problems
SILOG

DRINKS

DESSERT

TAPSILOG

KAPE

SAGING

TOSILOG

MILO

BROWNIES

LONGSILOG

ICED TEA

BANGSILOG

KAPE
BANGSILOG

SAGING
BROWNIES

MILO

SAGING
BROWNIES

ICED TEA

SAGING
BROWNIES
Fundamental Principle of Counting
TOSILOG

TAPSILOG
SAGING
KAPE

SAGING
KAPE

BROWNIES

BROWNIES

SAGING
MILO

BROWNIES

SAGING
MILO

BROWNIES

SAGING
ICED TEA

SAGING
ICED TEA

BROWNIES

BROWNIES

LONGSILOG

BANGSILOG

SAGING
KAPE

SAGING
KAPE

BROWNIES

BROWNIES

SAGING
MILO

BROWNIES

SAGING
MILO

SAGING
ICED TEA

BROWNIES
SAGING

ICED TEA

BROWNIES

There are 24 possible combo meals

BROWNIES
Fundamental Principle of Counting

The Product Rules
The Product Rule:
Suppose that a procedure can be
broken down into two successive
tasks. If there are n1 ways to do the
first task and n2 ways to do the second
task after the first task has been done,
then there are n1n2 ways to do the
procedure.
Introduction to Counting and Probability

The Product Rules

Generalized product rule:
If we have a procedure consisting of
sequential tasks T1, T2, …, Tn that can
be done in k1, k2, …, kn ways,
respectively, then there are n1  n2  … 
nm ways to carry out the procedure.
Introduction to Counting and Probability

Basic Counting Principles

The two product rules are
collectively called the
FUNDAMENTAL PRINCIPLE
OF COUNTING
Woohoo…
Introduction to Counting and Probability

The Product Rules
Generalized product rule:
If we have a procedure consisting of sequential tasks T1, T2, …, Tm that
can be done in k1, k2, …, kn ways, respectively, then there are n1  n2  … 
nm ways to carry out the procedure.

T1

k1

T2

k2

T3

k3

…

…

Tn

Tasks

kn

No. of
ways

no. of outcomes in all = k1k2k3 ...kn
Introduction to Counting and Probability

Basic Counting Principles

Example 1
If you have 5 T-shirts, 4 pairs of pants,
and 3 pairs of shoes, how many ways
can you choose to wear three of them?
Solution
The number of ways is

5  4  3   60
Introduction to Counting and Probability

Basic Counting Principles

Example 2
How many outcomes can you
have when you toss:
2 (head and tail)
a. One coin?
2x2=4
b. Two coins?
2x2x2=8
c. Three coins?
Introduction to Counting and Probability

Basic Counting Principles

Example 3
How many outcomes can you have
when you toss:
6
a. One die?
6 x 6 = 36
b. Two dice?
6 x 6 x 6 = 216
c. Three dice?
6 x 2 = 12
d. A die and a coin?
Fundamental Principle of Counting

Basic Counting Principles

Example 4
How many ways can you answer a
a. 20-item true or false quiz?
20 x 2 = 40

b.

20-item multiple choice test, with
choices A, B, C, D?
20 x 4 = 80
Fundamental Principle of Counting

Basic Counting Principles

Example 5
How many three-digit numbers
can form from the digits 1, 2, 3, 4
if the digits
a. can be repeated? 4 x 4 x 4 = 64
b. cannot be repeated?
4 x 3 x 2 = 24
Fundamental Principle of Counting

Basic Counting Principles

Example 7
How many three-digit EVEN
numbers can form from the digits
1, 2, 3, 4 if the digits
a. can be repeated? 4 x 4 x 2 = 32
b. cannot be repeated?
3 x 3 x 2 = 12
Introduction to Counting and Probability

Basic Counting Principles

Example 8
How many three-digit numbers
can form from the digits 0,1, 2, 3, 4
if the digits
a. can be repeated? 4 x 5 x 5 = 100
b. cannot be repeated?
4 x 4 x 3 = 48
Introduction to Counting and Probability

Check your understanding
1.
2.

3.

How many subdivision house numbers can
be issued using 1 letter and 3 digits?
How many ways can you choose one each
from 10 teachers, 7 staff, and 20 students
to go to an out-of-school meeting?
How many 4-digit numbers can be formed
from the digits 1 2, 3, 4, 5 if the digits cannot
be repeated?
Answers:

1. 26 x 10 x 10 x 10 = 26,000
2. 10 x 7 x 20 = 1,400
3. 5 x 4 x 3 x 2 = 120
Introduction to Counting and Probability

Basic Probability

Probability is a relative measure
of expectation or chance that
an event will occur.
Question: How likely is an event to
occur based on all the possible
outcomes?
Introduction to Counting and Probability

Basic Probability

Computing Probability
The probability p than an event can
occur is the ratio of the number of ways
that the event will occur over the
number of possible outcomes S.
number of ways that a certain event will occur
p
number of possible outcomes
Introduction to Counting and Probability

Basic Probability
Example 1
There are two outcomes in a toss of
a coin – head or tail. Thus, the
probability that a head will turn up in
a coin toss is 1 out of 2; that is,
number of heads
1
p

number of possible outcomes 2
Introduction to Counting and Probability

Basic Probability

Example 2
There are 6 outcomes in a roll of die.
What is the probability of getting a
a. 6?
One out of 6: p = 1/6
b. 2 or 3?
Two out of 6: p = 2/6 or 1/3
c. odd number? Three out of 6: p = 3/6 or 1/2
Zero out of 6: p = 0/6 or 0
d. 8?
Letter d is an IMPOSSIBLE EVENT
Introduction to Counting and Probability

Basic Probability

Example 3
A bowl has 5 blue balls, 6 red balls, and 4 green
balls. If you draw a ball at random, what is the
probability that you’ll
5 out of 15: p = 5/15 = 1/3
a.
get a blue ball?
6 out of 15: p = 6/15 = 2/5
b.
get a red ball?
4 out of 15: p = 4/15
c.
a green ball?
d.
not get a red ball? 5 + 4 = 9 out of 15: p = 9/15 or 3/5
e.
get a red or green ball?
6 + 4 = 10 out of 15:

p = 10/15 = 2/3
Introduction to Counting and Probability

Check your understanding
1.
2.
3.

Two coins are tossed. What is the
probability of getting two tails?
In a game of Bingo, what is the probability
that the first ball comes from the letter G?
All the three-digit numbers formed by using
the digits 1, 2, 3, and 4 without repeating
digits are put in a bowl. What is the
probability that when a number is drawn, it
is odd?
Introduction to Counting and Probability

Check your understanding
1. 1 out of 8:
p = 1/8
2. 10 out of 75: p = 10/75 = 2/15
3. Number of 3-digit numbers: 4 x

3x2

= 24
Number of odd 3-digit numbers:
3 x 2 x 2 = 12
p = 12/24 = 1/2

More Related Content

What's hot

Graphs of polynomial functions
Graphs of polynomial functionsGraphs of polynomial functions
Graphs of polynomial functionsCarlos Erepol
 
Graphs of linear equation
Graphs of linear equationGraphs of linear equation
Graphs of linear equationJunila Tejada
 
Permutation and combination
Permutation and combinationPermutation and combination
Permutation and combinationSadia Zareen
 
Adding and subtracting rational expressions
Adding and subtracting rational expressionsAdding and subtracting rational expressions
Adding and subtracting rational expressionsDawn Adams2
 
permutations power point
permutations power pointpermutations power point
permutations power pointAldrin Balenton
 
Introduction of Probability
Introduction of ProbabilityIntroduction of Probability
Introduction of Probabilityrey castro
 
Math 8 – triangle congruence, postulates,
Math 8 – triangle congruence, postulates,Math 8 – triangle congruence, postulates,
Math 8 – triangle congruence, postulates,Rebekah Andrea Fullido
 
5.1 sequences and summation notation
5.1 sequences and summation notation5.1 sequences and summation notation
5.1 sequences and summation notationmath260
 
Probability (gr.11)
Probability (gr.11)Probability (gr.11)
Probability (gr.11)Vukile Xhego
 
11.2 graphing linear equations in two variables
11.2 graphing linear equations in two variables11.2 graphing linear equations in two variables
11.2 graphing linear equations in two variablesGlenSchlee
 
Arithmetic sequence
Arithmetic sequenceArithmetic sequence
Arithmetic sequencemaricel mas
 
union and intersection of events.ppt
union and intersection of events.pptunion and intersection of events.ppt
union and intersection of events.pptIzah Catli
 

What's hot (20)

Graphs of polynomial functions
Graphs of polynomial functionsGraphs of polynomial functions
Graphs of polynomial functions
 
Graphs of linear equation
Graphs of linear equationGraphs of linear equation
Graphs of linear equation
 
Combination
CombinationCombination
Combination
 
Permutation and combination
Permutation and combinationPermutation and combination
Permutation and combination
 
Adding and subtracting rational expressions
Adding and subtracting rational expressionsAdding and subtracting rational expressions
Adding and subtracting rational expressions
 
Lesson 3: Limit Laws
Lesson 3: Limit LawsLesson 3: Limit Laws
Lesson 3: Limit Laws
 
joint variation
  joint variation  joint variation
joint variation
 
permutations power point
permutations power pointpermutations power point
permutations power point
 
Combination
CombinationCombination
Combination
 
Introduction of Probability
Introduction of ProbabilityIntroduction of Probability
Introduction of Probability
 
Math 8 – triangle congruence, postulates,
Math 8 – triangle congruence, postulates,Math 8 – triangle congruence, postulates,
Math 8 – triangle congruence, postulates,
 
Permutation
PermutationPermutation
Permutation
 
Circular permutation
Circular permutationCircular permutation
Circular permutation
 
5.1 sequences and summation notation
5.1 sequences and summation notation5.1 sequences and summation notation
5.1 sequences and summation notation
 
Probability (gr.11)
Probability (gr.11)Probability (gr.11)
Probability (gr.11)
 
Rectangular Coordinate System
Rectangular Coordinate SystemRectangular Coordinate System
Rectangular Coordinate System
 
11.2 graphing linear equations in two variables
11.2 graphing linear equations in two variables11.2 graphing linear equations in two variables
11.2 graphing linear equations in two variables
 
Harmonic sequence
Harmonic sequenceHarmonic sequence
Harmonic sequence
 
Arithmetic sequence
Arithmetic sequenceArithmetic sequence
Arithmetic sequence
 
union and intersection of events.ppt
union and intersection of events.pptunion and intersection of events.ppt
union and intersection of events.ppt
 

Viewers also liked

CABT Math 8 - Properties of Quadrilaterals
CABT Math 8 - Properties of QuadrilateralsCABT Math 8 - Properties of Quadrilaterals
CABT Math 8 - Properties of QuadrilateralsGilbert Joseph Abueg
 
CABT Math 8 measures of central tendency and dispersion
CABT Math 8   measures of central tendency and dispersionCABT Math 8   measures of central tendency and dispersion
CABT Math 8 measures of central tendency and dispersionGilbert Joseph Abueg
 
10 math pa_l_08-04
10 math pa_l_08-0410 math pa_l_08-04
10 math pa_l_08-04lkemper
 
Exponents, factors, and fractions math 7 chapter 2 review
Exponents, factors, and fractions  math 7 chapter 2 reviewExponents, factors, and fractions  math 7 chapter 2 review
Exponents, factors, and fractions math 7 chapter 2 reviewlashwnb
 
Jeopardy math 9 unit7 quiz
Jeopardy   math 9 unit7 quizJeopardy   math 9 unit7 quiz
Jeopardy math 9 unit7 quizSd 46
 
Math 7 geometry 03 angles and angle measurements
Math 7 geometry 03   angles and angle measurementsMath 7 geometry 03   angles and angle measurements
Math 7 geometry 03 angles and angle measurementsGilbert Joseph Abueg
 
Seige arndt-lightning talk swib13
Seige arndt-lightning talk swib13Seige arndt-lightning talk swib13
Seige arndt-lightning talk swib13Leander Seige
 
United states Historical Portraits
United states Historical PortraitsUnited states Historical Portraits
United states Historical PortraitsMelissa Forney
 
Solr fusion lt elag2014
Solr fusion lt elag2014Solr fusion lt elag2014
Solr fusion lt elag2014Leander Seige
 
VSB Military Law News Fall 2002
VSB Military Law News Fall 2002VSB Military Law News Fall 2002
VSB Military Law News Fall 2002davidbuzard
 
Its undergraduate-6734-2204109604-presentasi
Its undergraduate-6734-2204109604-presentasiIts undergraduate-6734-2204109604-presentasi
Its undergraduate-6734-2204109604-presentasiMuhamad Zamroni
 
Abuse of Natural Resources in Colombia
Abuse of Natural Resources in ColombiaAbuse of Natural Resources in Colombia
Abuse of Natural Resources in ColombiaJuan Garzon
 

Viewers also liked (20)

CABT Math 8 - Basics of Geometry
CABT Math 8 - Basics of GeometryCABT Math 8 - Basics of Geometry
CABT Math 8 - Basics of Geometry
 
CABT Math 8 - Properties of Quadrilaterals
CABT Math 8 - Properties of QuadrilateralsCABT Math 8 - Properties of Quadrilaterals
CABT Math 8 - Properties of Quadrilaterals
 
CABT Math 8 measures of central tendency and dispersion
CABT Math 8   measures of central tendency and dispersionCABT Math 8   measures of central tendency and dispersion
CABT Math 8 measures of central tendency and dispersion
 
10 math pa_l_08-04
10 math pa_l_08-0410 math pa_l_08-04
10 math pa_l_08-04
 
Exponents, factors, and fractions math 7 chapter 2 review
Exponents, factors, and fractions  math 7 chapter 2 reviewExponents, factors, and fractions  math 7 chapter 2 review
Exponents, factors, and fractions math 7 chapter 2 review
 
Jeopardy math 9 unit7 quiz
Jeopardy   math 9 unit7 quizJeopardy   math 9 unit7 quiz
Jeopardy math 9 unit7 quiz
 
Math 7 geometry 03 angles and angle measurements
Math 7 geometry 03   angles and angle measurementsMath 7 geometry 03   angles and angle measurements
Math 7 geometry 03 angles and angle measurements
 
Seige arndt-lightning talk swib13
Seige arndt-lightning talk swib13Seige arndt-lightning talk swib13
Seige arndt-lightning talk swib13
 
United states Historical Portraits
United states Historical PortraitsUnited states Historical Portraits
United states Historical Portraits
 
Stina ke bosso
Stina ke bossoStina ke bosso
Stina ke bosso
 
Rhashida a
Rhashida aRhashida a
Rhashida a
 
Solr fusion lt elag2014
Solr fusion lt elag2014Solr fusion lt elag2014
Solr fusion lt elag2014
 
PODEVOIP Empresa
PODEVOIP EmpresaPODEVOIP Empresa
PODEVOIP Empresa
 
Mooc
MoocMooc
Mooc
 
Advertising is Inception
Advertising is InceptionAdvertising is Inception
Advertising is Inception
 
PODEVOIP
PODEVOIPPODEVOIP
PODEVOIP
 
VSB Military Law News Fall 2002
VSB Military Law News Fall 2002VSB Military Law News Fall 2002
VSB Military Law News Fall 2002
 
Its undergraduate-6734-2204109604-presentasi
Its undergraduate-6734-2204109604-presentasiIts undergraduate-6734-2204109604-presentasi
Its undergraduate-6734-2204109604-presentasi
 
Abuse of Natural Resources in Colombia
Abuse of Natural Resources in ColombiaAbuse of Natural Resources in Colombia
Abuse of Natural Resources in Colombia
 
El uso de internet en la educación
El uso de internet en la educaciónEl uso de internet en la educación
El uso de internet en la educación
 

Similar to CABT Math 8 - Fundamental Principle of Counting

statiscs and probability math college to help student
statiscs and probability math college  to help studentstatiscs and probability math college  to help student
statiscs and probability math college to help studentcharlezeannprodonram
 
Basic Counting Law Discrete Math Power Point Presentaton
Basic Counting Law Discrete Math Power Point PresentatonBasic Counting Law Discrete Math Power Point Presentaton
Basic Counting Law Discrete Math Power Point Presentatonedzhoroevastudy
 
Probability power point combo from holt ch 10
Probability power point combo from holt ch 10Probability power point combo from holt ch 10
Probability power point combo from holt ch 10lothomas
 
Simple probability
Simple probabilitySimple probability
Simple probability06426345
 
Beginners counting and probability.pptx
Beginners counting and probability.pptxBeginners counting and probability.pptx
Beginners counting and probability.pptxAbbyXiong
 
7.8 simple probability 1
7.8 simple probability   17.8 simple probability   1
7.8 simple probability 1bweldon
 
Counting Partitions: Combinations - Finite Math
Counting Partitions: Combinations - Finite MathCounting Partitions: Combinations - Finite Math
Counting Partitions: Combinations - Finite MathJustin Tallant
 
permutations-and-combinations.ppt
permutations-and-combinations.pptpermutations-and-combinations.ppt
permutations-and-combinations.pptBryanlibrado
 
AII12_Permutations_Combinations.ppt
AII12_Permutations_Combinations.pptAII12_Permutations_Combinations.ppt
AII12_Permutations_Combinations.pptLaeGadgude
 
permutations-and-combinations.ppt
permutations-and-combinations.pptpermutations-and-combinations.ppt
permutations-and-combinations.pptBryanlibrado
 
permutations-and-combinations.ppt
permutations-and-combinations.pptpermutations-and-combinations.ppt
permutations-and-combinations.pptJewelEstrada
 
permutations and combinations.ppt
permutations and combinations.pptpermutations and combinations.ppt
permutations and combinations.pptBryanlibrado
 
Permutations and Combinations
Permutations and CombinationsPermutations and Combinations
Permutations and CombinationsAngel Willis
 
(7) Lesson 9.1
(7) Lesson 9.1(7) Lesson 9.1
(7) Lesson 9.1wzuri
 
Algebra unit 9.7
Algebra unit 9.7Algebra unit 9.7
Algebra unit 9.7Mark Ryder
 
counting techniques
counting techniquescounting techniques
counting techniquesUnsa Shakir
 
permutations-and-combinations for Quantitative Reasoning Class
permutations-and-combinations for Quantitative Reasoning Classpermutations-and-combinations for Quantitative Reasoning Class
permutations-and-combinations for Quantitative Reasoning ClassMrsWALKERRICHARDSON
 
lesson4-intrduction to probability grade10
lesson4-intrduction to probability grade10lesson4-intrduction to probability grade10
lesson4-intrduction to probability grade10CharlesIanVArnado
 

Similar to CABT Math 8 - Fundamental Principle of Counting (20)

statiscs and probability math college to help student
statiscs and probability math college  to help studentstatiscs and probability math college  to help student
statiscs and probability math college to help student
 
Basic Counting Law Discrete Math Power Point Presentaton
Basic Counting Law Discrete Math Power Point PresentatonBasic Counting Law Discrete Math Power Point Presentaton
Basic Counting Law Discrete Math Power Point Presentaton
 
Probability power point combo from holt ch 10
Probability power point combo from holt ch 10Probability power point combo from holt ch 10
Probability power point combo from holt ch 10
 
Simple probability
Simple probabilitySimple probability
Simple probability
 
Beginners counting and probability.pptx
Beginners counting and probability.pptxBeginners counting and probability.pptx
Beginners counting and probability.pptx
 
PPT8.ppt
PPT8.pptPPT8.ppt
PPT8.ppt
 
Counting
CountingCounting
Counting
 
7.8 simple probability 1
7.8 simple probability   17.8 simple probability   1
7.8 simple probability 1
 
Counting Partitions: Combinations - Finite Math
Counting Partitions: Combinations - Finite MathCounting Partitions: Combinations - Finite Math
Counting Partitions: Combinations - Finite Math
 
permutations-and-combinations.ppt
permutations-and-combinations.pptpermutations-and-combinations.ppt
permutations-and-combinations.ppt
 
AII12_Permutations_Combinations.ppt
AII12_Permutations_Combinations.pptAII12_Permutations_Combinations.ppt
AII12_Permutations_Combinations.ppt
 
permutations-and-combinations.ppt
permutations-and-combinations.pptpermutations-and-combinations.ppt
permutations-and-combinations.ppt
 
permutations-and-combinations.ppt
permutations-and-combinations.pptpermutations-and-combinations.ppt
permutations-and-combinations.ppt
 
permutations and combinations.ppt
permutations and combinations.pptpermutations and combinations.ppt
permutations and combinations.ppt
 
Permutations and Combinations
Permutations and CombinationsPermutations and Combinations
Permutations and Combinations
 
(7) Lesson 9.1
(7) Lesson 9.1(7) Lesson 9.1
(7) Lesson 9.1
 
Algebra unit 9.7
Algebra unit 9.7Algebra unit 9.7
Algebra unit 9.7
 
counting techniques
counting techniquescounting techniques
counting techniques
 
permutations-and-combinations for Quantitative Reasoning Class
permutations-and-combinations for Quantitative Reasoning Classpermutations-and-combinations for Quantitative Reasoning Class
permutations-and-combinations for Quantitative Reasoning Class
 
lesson4-intrduction to probability grade10
lesson4-intrduction to probability grade10lesson4-intrduction to probability grade10
lesson4-intrduction to probability grade10
 

More from Gilbert Joseph Abueg

CABT Math 8 - Angles and Angle Measurements
CABT Math 8 - Angles and Angle MeasurementsCABT Math 8 - Angles and Angle Measurements
CABT Math 8 - Angles and Angle MeasurementsGilbert Joseph Abueg
 
Math Reviewer - Word Problems in Algebra
Math Reviewer - Word Problems in AlgebraMath Reviewer - Word Problems in Algebra
Math Reviewer - Word Problems in AlgebraGilbert Joseph Abueg
 
Math-tanong CEER 2012 - Set 1 Solutions
Math-tanong CEER 2012 - Set 1 SolutionsMath-tanong CEER 2012 - Set 1 Solutions
Math-tanong CEER 2012 - Set 1 SolutionsGilbert Joseph Abueg
 
Math-tanong CEER 2012 - Set 1 solutions
Math-tanong CEER 2012 - Set 1 solutionsMath-tanong CEER 2012 - Set 1 solutions
Math-tanong CEER 2012 - Set 1 solutionsGilbert Joseph Abueg
 

More from Gilbert Joseph Abueg (7)

CABT Math 8 - Angles and Angle Measurements
CABT Math 8 - Angles and Angle MeasurementsCABT Math 8 - Angles and Angle Measurements
CABT Math 8 - Angles and Angle Measurements
 
Math Reviewer - Word Problems in Algebra
Math Reviewer - Word Problems in AlgebraMath Reviewer - Word Problems in Algebra
Math Reviewer - Word Problems in Algebra
 
Math-tanong CEER 2012 - Set 2
Math-tanong CEER 2012 - Set 2Math-tanong CEER 2012 - Set 2
Math-tanong CEER 2012 - Set 2
 
Math-tanong CEER 2012 - Set 1 Solutions
Math-tanong CEER 2012 - Set 1 SolutionsMath-tanong CEER 2012 - Set 1 Solutions
Math-tanong CEER 2012 - Set 1 Solutions
 
Math-tanong CEER 2012 - Set 1 solutions
Math-tanong CEER 2012 - Set 1 solutionsMath-tanong CEER 2012 - Set 1 solutions
Math-tanong CEER 2012 - Set 1 solutions
 
Math-tanong CEER 2012 - Set 1
Math-tanong CEER 2012 - Set 1Math-tanong CEER 2012 - Set 1
Math-tanong CEER 2012 - Set 1
 
CEER 2012 Math Lecture
CEER 2012 Math LectureCEER 2012 Math Lecture
CEER 2012 Math Lecture
 

Recently uploaded

Virtual-Orientation-on-the-Administration-of-NATG12-NATG6-and-ELLNA.pdf
Virtual-Orientation-on-the-Administration-of-NATG12-NATG6-and-ELLNA.pdfVirtual-Orientation-on-the-Administration-of-NATG12-NATG6-and-ELLNA.pdf
Virtual-Orientation-on-the-Administration-of-NATG12-NATG6-and-ELLNA.pdfErwinPantujan2
 
Integumentary System SMP B. Pharm Sem I.ppt
Integumentary System SMP B. Pharm Sem I.pptIntegumentary System SMP B. Pharm Sem I.ppt
Integumentary System SMP B. Pharm Sem I.pptshraddhaparab530
 
Barangay Council for the Protection of Children (BCPC) Orientation.pptx
Barangay Council for the Protection of Children (BCPC) Orientation.pptxBarangay Council for the Protection of Children (BCPC) Orientation.pptx
Barangay Council for the Protection of Children (BCPC) Orientation.pptxCarlos105
 
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)lakshayb543
 
Keynote by Prof. Wurzer at Nordex about IP-design
Keynote by Prof. Wurzer at Nordex about IP-designKeynote by Prof. Wurzer at Nordex about IP-design
Keynote by Prof. Wurzer at Nordex about IP-designMIPLM
 
GRADE 4 - SUMMATIVE TEST QUARTER 4 ALL SUBJECTS
GRADE 4 - SUMMATIVE TEST QUARTER 4 ALL SUBJECTSGRADE 4 - SUMMATIVE TEST QUARTER 4 ALL SUBJECTS
GRADE 4 - SUMMATIVE TEST QUARTER 4 ALL SUBJECTSJoshuaGantuangco2
 
Music 9 - 4th quarter - Vocal Music of the Romantic Period.pptx
Music 9 - 4th quarter - Vocal Music of the Romantic Period.pptxMusic 9 - 4th quarter - Vocal Music of the Romantic Period.pptx
Music 9 - 4th quarter - Vocal Music of the Romantic Period.pptxleah joy valeriano
 
Inclusivity Essentials_ Creating Accessible Websites for Nonprofits .pdf
Inclusivity Essentials_ Creating Accessible Websites for Nonprofits .pdfInclusivity Essentials_ Creating Accessible Websites for Nonprofits .pdf
Inclusivity Essentials_ Creating Accessible Websites for Nonprofits .pdfTechSoup
 
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptxQ4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptxlancelewisportillo
 
ANG SEKTOR NG agrikultura.pptx QUARTER 4
ANG SEKTOR NG agrikultura.pptx QUARTER 4ANG SEKTOR NG agrikultura.pptx QUARTER 4
ANG SEKTOR NG agrikultura.pptx QUARTER 4MiaBumagat1
 
AUDIENCE THEORY -CULTIVATION THEORY - GERBNER.pptx
AUDIENCE THEORY -CULTIVATION THEORY -  GERBNER.pptxAUDIENCE THEORY -CULTIVATION THEORY -  GERBNER.pptx
AUDIENCE THEORY -CULTIVATION THEORY - GERBNER.pptxiammrhaywood
 
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - CẢ NĂ...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - CẢ NĂ...HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - CẢ NĂ...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - CẢ NĂ...Nguyen Thanh Tu Collection
 
Difference Between Search & Browse Methods in Odoo 17
Difference Between Search & Browse Methods in Odoo 17Difference Between Search & Browse Methods in Odoo 17
Difference Between Search & Browse Methods in Odoo 17Celine George
 
How to do quick user assign in kanban in Odoo 17 ERP
How to do quick user assign in kanban in Odoo 17 ERPHow to do quick user assign in kanban in Odoo 17 ERP
How to do quick user assign in kanban in Odoo 17 ERPCeline George
 
What is Model Inheritance in Odoo 17 ERP
What is Model Inheritance in Odoo 17 ERPWhat is Model Inheritance in Odoo 17 ERP
What is Model Inheritance in Odoo 17 ERPCeline George
 
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptxMULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptxAnupkumar Sharma
 
Field Attribute Index Feature in Odoo 17
Field Attribute Index Feature in Odoo 17Field Attribute Index Feature in Odoo 17
Field Attribute Index Feature in Odoo 17Celine George
 
Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...Seán Kennedy
 
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATIONTHEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATIONHumphrey A Beña
 

Recently uploaded (20)

Virtual-Orientation-on-the-Administration-of-NATG12-NATG6-and-ELLNA.pdf
Virtual-Orientation-on-the-Administration-of-NATG12-NATG6-and-ELLNA.pdfVirtual-Orientation-on-the-Administration-of-NATG12-NATG6-and-ELLNA.pdf
Virtual-Orientation-on-the-Administration-of-NATG12-NATG6-and-ELLNA.pdf
 
Integumentary System SMP B. Pharm Sem I.ppt
Integumentary System SMP B. Pharm Sem I.pptIntegumentary System SMP B. Pharm Sem I.ppt
Integumentary System SMP B. Pharm Sem I.ppt
 
Barangay Council for the Protection of Children (BCPC) Orientation.pptx
Barangay Council for the Protection of Children (BCPC) Orientation.pptxBarangay Council for the Protection of Children (BCPC) Orientation.pptx
Barangay Council for the Protection of Children (BCPC) Orientation.pptx
 
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
Visit to a blind student's school🧑‍🦯🧑‍🦯(community medicine)
 
Keynote by Prof. Wurzer at Nordex about IP-design
Keynote by Prof. Wurzer at Nordex about IP-designKeynote by Prof. Wurzer at Nordex about IP-design
Keynote by Prof. Wurzer at Nordex about IP-design
 
GRADE 4 - SUMMATIVE TEST QUARTER 4 ALL SUBJECTS
GRADE 4 - SUMMATIVE TEST QUARTER 4 ALL SUBJECTSGRADE 4 - SUMMATIVE TEST QUARTER 4 ALL SUBJECTS
GRADE 4 - SUMMATIVE TEST QUARTER 4 ALL SUBJECTS
 
Music 9 - 4th quarter - Vocal Music of the Romantic Period.pptx
Music 9 - 4th quarter - Vocal Music of the Romantic Period.pptxMusic 9 - 4th quarter - Vocal Music of the Romantic Period.pptx
Music 9 - 4th quarter - Vocal Music of the Romantic Period.pptx
 
Inclusivity Essentials_ Creating Accessible Websites for Nonprofits .pdf
Inclusivity Essentials_ Creating Accessible Websites for Nonprofits .pdfInclusivity Essentials_ Creating Accessible Websites for Nonprofits .pdf
Inclusivity Essentials_ Creating Accessible Websites for Nonprofits .pdf
 
YOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptx
YOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptxYOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptx
YOUVE_GOT_EMAIL_PRELIMS_EL_DORADO_2024.pptx
 
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptxQ4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
Q4-PPT-Music9_Lesson-1-Romantic-Opera.pptx
 
ANG SEKTOR NG agrikultura.pptx QUARTER 4
ANG SEKTOR NG agrikultura.pptx QUARTER 4ANG SEKTOR NG agrikultura.pptx QUARTER 4
ANG SEKTOR NG agrikultura.pptx QUARTER 4
 
AUDIENCE THEORY -CULTIVATION THEORY - GERBNER.pptx
AUDIENCE THEORY -CULTIVATION THEORY -  GERBNER.pptxAUDIENCE THEORY -CULTIVATION THEORY -  GERBNER.pptx
AUDIENCE THEORY -CULTIVATION THEORY - GERBNER.pptx
 
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - CẢ NĂ...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - CẢ NĂ...HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - CẢ NĂ...
HỌC TỐT TIẾNG ANH 11 THEO CHƯƠNG TRÌNH GLOBAL SUCCESS ĐÁP ÁN CHI TIẾT - CẢ NĂ...
 
Difference Between Search & Browse Methods in Odoo 17
Difference Between Search & Browse Methods in Odoo 17Difference Between Search & Browse Methods in Odoo 17
Difference Between Search & Browse Methods in Odoo 17
 
How to do quick user assign in kanban in Odoo 17 ERP
How to do quick user assign in kanban in Odoo 17 ERPHow to do quick user assign in kanban in Odoo 17 ERP
How to do quick user assign in kanban in Odoo 17 ERP
 
What is Model Inheritance in Odoo 17 ERP
What is Model Inheritance in Odoo 17 ERPWhat is Model Inheritance in Odoo 17 ERP
What is Model Inheritance in Odoo 17 ERP
 
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptxMULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
MULTIDISCIPLINRY NATURE OF THE ENVIRONMENTAL STUDIES.pptx
 
Field Attribute Index Feature in Odoo 17
Field Attribute Index Feature in Odoo 17Field Attribute Index Feature in Odoo 17
Field Attribute Index Feature in Odoo 17
 
Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...Student Profile Sample - We help schools to connect the data they have, with ...
Student Profile Sample - We help schools to connect the data they have, with ...
 
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATIONTHEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
THEORIES OF ORGANIZATION-PUBLIC ADMINISTRATION
 

CABT Math 8 - Fundamental Principle of Counting

  • 1.
  • 2.
  • 3. Introduction to Counting and Probability Some Terms “Probability is the branch of mathematics that provide quantitative description of the likely occurrence of an event. Outcome – any possible result of an experiment or operation Sample space – the complete list of all possible outcomes of an experiment or operation Event – refers to any subset of a sample space Counting – operation used to find the number of possible outcomes
  • 4. Introduction to Counting and Probability Counting Problems Counting problems are of the following kind: “How many combinations can I make with 5 Tshirts, 4 pairs of pants, and 3 kinds of shoes? “How many ways are there to pick starting 5 players out of a 12-player basketball team?” Most importantly, counting is the basis for computing probabilities. Example;:“What is the probability of winning the lotto?”
  • 5. Introduction to Counting and Probability Counting Problems Example: Ang Carinderia ni Jay ay may breakfast promo kung saan maaari kang makabuo ng combo meal mula sa mga sumusunod: SILOG DRINKS DESSERT TAPSILOG KAPE SAGING TOSILOG MILO BROWNIES LONGSILOG ICED TEA BANGSILOG
  • 6. Introduction to Counting and Probability Counting Problems Example: Question: If you want to create a combo meal by choose one of each kind, how many choices can you have? SILOG DRINKS DESSERT TAPSILOG KAPE SAGING TOSILOG MILO BROWNIES LONGSILOG ICED TEA BANGSILOG
  • 7. Introduction to Counting and Probability Counting Problems SILOG DRINKS DESSERT TAPSILOG KAPE SAGING TOSILOG MILO BROWNIES LONGSILOG ICED TEA BANGSILOG KAPE TAPSILOG SAGING BROWNIES MILO SAGING BROWNIES ICED TEA SAGING BROWNIES
  • 8. Introduction to Counting and Probability Counting Problems SILOG DRINKS DESSERT TAPSILOG KAPE SAGING TOSILOG MILO BROWNIES LONGSILOG ICED TEA BANGSILOG KAPE TOSILOG SAGING BROWNIES MILO SAGING BROWNIES ICED TEA SAGING BROWNIES
  • 9. Introduction to Counting and Probability Counting Problems SILOG DRINKS DESSERT TAPSILOG KAPE SAGING TOSILOG MILO BROWNIES LONGSILOG ICED TEA BANGSILOG KAPE LONGSILOG SAGING BROWNIES MILO SAGING BROWNIES ICED TEA SAGING BROWNIES
  • 10. Introduction to Counting and Probability Counting Problems SILOG DRINKS DESSERT TAPSILOG KAPE SAGING TOSILOG MILO BROWNIES LONGSILOG ICED TEA BANGSILOG KAPE BANGSILOG SAGING BROWNIES MILO SAGING BROWNIES ICED TEA SAGING BROWNIES
  • 11. Fundamental Principle of Counting TOSILOG TAPSILOG SAGING KAPE SAGING KAPE BROWNIES BROWNIES SAGING MILO BROWNIES SAGING MILO BROWNIES SAGING ICED TEA SAGING ICED TEA BROWNIES BROWNIES LONGSILOG BANGSILOG SAGING KAPE SAGING KAPE BROWNIES BROWNIES SAGING MILO BROWNIES SAGING MILO SAGING ICED TEA BROWNIES SAGING ICED TEA BROWNIES There are 24 possible combo meals BROWNIES
  • 12. Fundamental Principle of Counting The Product Rules The Product Rule: Suppose that a procedure can be broken down into two successive tasks. If there are n1 ways to do the first task and n2 ways to do the second task after the first task has been done, then there are n1n2 ways to do the procedure.
  • 13. Introduction to Counting and Probability The Product Rules Generalized product rule: If we have a procedure consisting of sequential tasks T1, T2, …, Tn that can be done in k1, k2, …, kn ways, respectively, then there are n1  n2  …  nm ways to carry out the procedure.
  • 14. Introduction to Counting and Probability Basic Counting Principles The two product rules are collectively called the FUNDAMENTAL PRINCIPLE OF COUNTING Woohoo…
  • 15. Introduction to Counting and Probability The Product Rules Generalized product rule: If we have a procedure consisting of sequential tasks T1, T2, …, Tm that can be done in k1, k2, …, kn ways, respectively, then there are n1  n2  …  nm ways to carry out the procedure. T1 k1 T2 k2 T3 k3 … … Tn Tasks kn No. of ways no. of outcomes in all = k1k2k3 ...kn
  • 16. Introduction to Counting and Probability Basic Counting Principles Example 1 If you have 5 T-shirts, 4 pairs of pants, and 3 pairs of shoes, how many ways can you choose to wear three of them? Solution The number of ways is 5  4  3   60
  • 17. Introduction to Counting and Probability Basic Counting Principles Example 2 How many outcomes can you have when you toss: 2 (head and tail) a. One coin? 2x2=4 b. Two coins? 2x2x2=8 c. Three coins?
  • 18. Introduction to Counting and Probability Basic Counting Principles Example 3 How many outcomes can you have when you toss: 6 a. One die? 6 x 6 = 36 b. Two dice? 6 x 6 x 6 = 216 c. Three dice? 6 x 2 = 12 d. A die and a coin?
  • 19. Fundamental Principle of Counting Basic Counting Principles Example 4 How many ways can you answer a a. 20-item true or false quiz? 20 x 2 = 40 b. 20-item multiple choice test, with choices A, B, C, D? 20 x 4 = 80
  • 20. Fundamental Principle of Counting Basic Counting Principles Example 5 How many three-digit numbers can form from the digits 1, 2, 3, 4 if the digits a. can be repeated? 4 x 4 x 4 = 64 b. cannot be repeated? 4 x 3 x 2 = 24
  • 21. Fundamental Principle of Counting Basic Counting Principles Example 7 How many three-digit EVEN numbers can form from the digits 1, 2, 3, 4 if the digits a. can be repeated? 4 x 4 x 2 = 32 b. cannot be repeated? 3 x 3 x 2 = 12
  • 22. Introduction to Counting and Probability Basic Counting Principles Example 8 How many three-digit numbers can form from the digits 0,1, 2, 3, 4 if the digits a. can be repeated? 4 x 5 x 5 = 100 b. cannot be repeated? 4 x 4 x 3 = 48
  • 23. Introduction to Counting and Probability Check your understanding 1. 2. 3. How many subdivision house numbers can be issued using 1 letter and 3 digits? How many ways can you choose one each from 10 teachers, 7 staff, and 20 students to go to an out-of-school meeting? How many 4-digit numbers can be formed from the digits 1 2, 3, 4, 5 if the digits cannot be repeated? Answers: 1. 26 x 10 x 10 x 10 = 26,000 2. 10 x 7 x 20 = 1,400 3. 5 x 4 x 3 x 2 = 120
  • 24. Introduction to Counting and Probability Basic Probability Probability is a relative measure of expectation or chance that an event will occur. Question: How likely is an event to occur based on all the possible outcomes?
  • 25. Introduction to Counting and Probability Basic Probability Computing Probability The probability p than an event can occur is the ratio of the number of ways that the event will occur over the number of possible outcomes S. number of ways that a certain event will occur p number of possible outcomes
  • 26. Introduction to Counting and Probability Basic Probability Example 1 There are two outcomes in a toss of a coin – head or tail. Thus, the probability that a head will turn up in a coin toss is 1 out of 2; that is, number of heads 1 p  number of possible outcomes 2
  • 27. Introduction to Counting and Probability Basic Probability Example 2 There are 6 outcomes in a roll of die. What is the probability of getting a a. 6? One out of 6: p = 1/6 b. 2 or 3? Two out of 6: p = 2/6 or 1/3 c. odd number? Three out of 6: p = 3/6 or 1/2 Zero out of 6: p = 0/6 or 0 d. 8? Letter d is an IMPOSSIBLE EVENT
  • 28. Introduction to Counting and Probability Basic Probability Example 3 A bowl has 5 blue balls, 6 red balls, and 4 green balls. If you draw a ball at random, what is the probability that you’ll 5 out of 15: p = 5/15 = 1/3 a. get a blue ball? 6 out of 15: p = 6/15 = 2/5 b. get a red ball? 4 out of 15: p = 4/15 c. a green ball? d. not get a red ball? 5 + 4 = 9 out of 15: p = 9/15 or 3/5 e. get a red or green ball? 6 + 4 = 10 out of 15: p = 10/15 = 2/3
  • 29. Introduction to Counting and Probability Check your understanding 1. 2. 3. Two coins are tossed. What is the probability of getting two tails? In a game of Bingo, what is the probability that the first ball comes from the letter G? All the three-digit numbers formed by using the digits 1, 2, 3, and 4 without repeating digits are put in a bowl. What is the probability that when a number is drawn, it is odd?
  • 30. Introduction to Counting and Probability Check your understanding 1. 1 out of 8: p = 1/8 2. 10 out of 75: p = 10/75 = 2/15 3. Number of 3-digit numbers: 4 x 3x2 = 24 Number of odd 3-digit numbers: 3 x 2 x 2 = 12 p = 12/24 = 1/2