WARMUPS [(9-5) x 6] + 42 x 3 = IN 1996 780,000,000 CDs WERE

SHIPPED IN THE U.S.. WHAT IS ANOTHER WAY OF EXPESSING THIS LARGE NUMBER?

COUNTING

CHAPTER 10-5

COUNTING

USED TO DETERMINE POSSIBLE STATISTICAL OUTCOMES

PROCESS USED IN GENETIC ENGINEERING

USED IN GROWING PLANTS TELLS US HOW MANY WAYS THINGS

CAN BE COMBINED

TWO METHODS OF ìCOUNTINGî

TREE DIAGRAMS FUNDAMENTAL

COUNTING PRINCIPLE

TWO METHODS OF ìCOUNTINGî

TREE DIAGRAMS FUNDAMENTAL

COUNTING PRINCIPLE

TREE DIAGRAM

A TREE DIAGRAM IS A LINE SCHEMATIC THAT LINKS ALL POSSIBLE OUTCOMES

X AX

A Y AY

Z AZ

X BX

B Y BY

Z BZ

TREE DIAGRAM

IF MEL HAS TWO CARS WITH THE OPTION OF THREE COLORS. WHAT IS THE POSSIBLE CAR COLOR COMBINATIONS ARE THERE

TREE DIAGRAM

IF MEL HAS TWO CARS WITH THE OPTION OF THREE COLORS. WHAT IS THE POSSIBLE CAR COLOR COMBINATIONS ARE THERE

RED HONDA/RED

HONDA

TREE DIAGRAM

IF MEL HAS TWO CARS WITH THE OPTION OF THREE COLORS. WHAT IS THE POSSIBLE CAR COLOR COMBINATIONS ARE THERE

RED HONDA/RED

HONDA BLUE HONDA/BLUE

TREE DIAGRAM

IF MEL HAS TWO CARS WITH THE OPTION OF THREE COLORS. WHAT IS THE POSSIBLE CAR COLOR COMBINATIONS ARE THERE

RED HONDA/RED

HONDA BLUE HONDA/BLUE

GREEN HONDA/GREEN

TREE DIAGRAM

IF MEL HAS TWO CARS WITH THE OPTION OF THREE COLORS. WHAT IS THE POSSIBLE CAR COLOR COMBINATIONS ARE THERE

RED HONDA/RED

HONDA BLUE HONDA/BLUE

GREEN HONDA/GREEN

RED FORD/RED

FORD

TREE DIAGRAM

IF MEL HAS TWO CARS WITH THE OPTION OF THREE COLORS. WHAT IS THE POSSIBLE CAR COLOR COMBINATIONS ARE THERE

RED HONDA/RED

HONDA BLUE HONDA/BLUE

GREEN HONDA/GREEN

RED FORD/RED

FORD BLUE FORD/BLUE

TREE DIAGRAM

IF MEL HAS TWO CARS WITH THE OPTION OF THREE COLORS. WHAT IS THE POSSIBLE CAR COLOR COMBINATIONS ARE THERE?

RED HONDA/RED

HONDA BLUE HONDA/BLUE

GREEN HONDA/GREEN

RED FORD/RED

FORD BLUE FORD/BLUE

GREEN FORD/GREEM

TREE DIAGRAM IF MEL HAS TWO

CARS WITH THE OPTION OF THREE COLORS. WHAT IS THE POSSIBLE CAR COLOR COMBINATIONS ARE THERE?

THERE ARE 6 POSSIBLE OUTCOMES

RED HONDA/RED

HONDA BLUE HONDA/BLUE

GREEN HONDA/GREEN

RED FORD/RED

FORD BLUE FORD/BLUE

GREEN FORD/GREEM

TWO METHODS OF ìCOUNTINGî

TREE DIAGRAMS FUNDAMENTAL

COUNTING PRINCIPLE

FUNDAMENTAL COUNTING PRINCIPLE

IF EVENT M CAN OCCUR IN m WAYS, IS FOLLOWED BY EVENT N THAT CAN OCCUR IN n WAYS, THEN THE EVENT M FOLLOWED BY EVENT N CAN OCCUR IN m TIMES n WAYS.

FUNDAMENTAL COUNTING PRINCIPLE

SUPPOSE I HAVE 6 DIFFERENT CAR MODELS AND 9 DIFFERENT PAINT SCHEMES. HOW MAY DIFFERENT CAR/PAINT COMBINATIONS CAN I HAVE?

FUNDAMENTAL COUNTING PRINCIPLE

SUPPOSE I HAVE 6 DIFFERENT CAR MODELS AND 9 DIFFERENT PAINT SCHEMES. HOW MAY DIFFERENT CAR/PAINT COMBINATIONS CAN I HAVE?

9 6 54x

YOU DO THE MATH

YOU DO THE MATH

A DICE IS ROLLED TWICE. HOW MANY POSSIBLE OUTCOMES ARE THERE?

YOU DO THE MATH

1 11

2 12

1 3 13

4 14

5 15

6 16

YOU DO THE MATH

1 11

2 12

1 3 13

4 14

5 15

6 16

6 POSSIBILITIES

YOU DO THE MATH

1 21

2 22

2 3 23

4 24

5 25

6 26

YOU DO THE MATH

1 21

2 22

2 3 23

4 24

5 25

6 26

6 POSSIBILITIES

YOU DO THE MATH

1 31

2 32

3 3 33

4 34

5 35

6 36

YOU DO THE MATH

1 31

2 32

3 3 33

4 34

5 35

6 36

6 POSSIBILITIES

YOU DO THE MATH

1 41

2 42

4 3 43

4 44

5 45

6 46

YOU DO THE MATH

1 41

2 42

4 3 43

4 44

5 45

6 46

6 POSSIBILITIES

YOU DO THE MATH

1 51

2 52

5 3 53

4 54

5 55

6 56

YOU DO THE MATH

1 51

2 52

5 3 53

4 54

5 55

6 56

6 POSSIBILITIES

YOU DO THE MATH

1 61

2 62

6 3 63

4 64

5 65

6 66

YOU DO THE MATH

1 61

2 62

6 3 63

4 64

5 65

6 66

6 POSSIBILITIES

ALL TOGETHER

FOR 1’S - 6 POSSIBILITIES FOR 2’S - 6 POSSIBLITIES FOR 3’S - 6 POSSIBILITIES FOR 4’S - 6 POSSIBILITIES FOR 5’S - 6 POSSIBILITIES FOR 6’S - 6 POSSIBILITIES

ALL TOGETHER

FOR 1’S - 6 POSSIBILITIES FOR 2’S - 6 POSSIBLITIES FOR 3’S - 6 POSSIBILITIES FOR 4’S - 6 POSSIBILITIES FOR 5’S - 6 POSSIBILITIES FOR 6’S - 6 POSSIBILITIES

TOTAL OF

36 POSSIBILITIES

IN ALL

36 POSSIBILITIES

1,1 1,2 1,3 1,4 1,5 1,6

2,1 2,2 2,3 2,4 2,5 2,6

3,1 3,2 3,3 3,4 3,5 3,6

4,1 4,2 4,3 4,4 4,5 4,6

5,1 5,2 5,3 5,4 5,5 5,6

6,1 6,2 6,3 6,4 6,5 6,6

PROBABILITY

PROBABILTIY IS THE CHANCE AN EVENT WILL HAPPEN

PROBABILITY = NUMBER OF FAVORABLE OUTCOMES DIVIDED BY POSSIBLE OUTCOMES

YOU DO THE MATH

A DICE IS ROLLED TWICE. WE FOUND OUT THAT THERE WERE 36 POSSIBLE OUTCOMES.

WHAT IS THE PROBABILITY OF ROLLING TWO 1’S?

PROBABILITY PROBABILITY = FAVORABLE OUTCOMES POSSIBLE OUTCOMES

PROBABILITY = 1 36

1/36 OR 1:36 OR .027

HOMEWORK

HOMEWORK

HOMEWORK PAGE 649-650; DO 1-9 IF YOU CAN DO THESE

YOU ARE A SUPER MATHEMATICIAN

HOMEWORK: PAGE 650; 8-9; AND 16-19.