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Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A...

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Tree Diagrams Mrs. Poland September 21, 2009 Tuesday, February 9, 2010
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Page 1: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

Tree Diagrams

Mrs. Poland

September 21, 2009

Tuesday, February 9, 2010

Page 2: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

A tree diagram is a way of describing all the

possible outcomes from a series of events

A tree diagram is a way of calculating the probability of

all the possible outcomes from a series of events

Tuesday, February 9, 2010

Page 3: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

What is a tree diagram?

• There are many ways to count the number of outcomes for specific events, the simplest way is to use a tree diagram. To make a tree diagram, you must have a separate branch for every choice made.

3

Tuesday, February 9, 2010

Page 4: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

A list of possible events could include

• Taking a sweet from a jar of red, yellow and green sweets

• Flipping a coin

• Picking a square on a chess board

All these events have definite outcomes

Black or white

Head or tail

What is different about the outcome here?Red, yellow or green

There are 3 outcomes

Tuesday, February 9, 2010

Page 5: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

Each event can be represented by a tree diagram

Picking a square on a chess board

BLACK

WHITE

The diagram shows you have a choice of 2 paths (branches)

Flipping a coin

HEAD

TAIL

The diagram shows you have a choice of 2 paths (branches)

Picking a sweet from a jar containing red, yellow and green sweets

REMEMBER – there are 3 outcomes

RED

YELLOW

GREEN

The diagram shows you have a choice of 3 paths (branches)

Tuesday, February 9, 2010

Page 6: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

Similarly, the tree diagram for flipping a coin is

Tails

Heads

Tuesday, February 9, 2010

Page 7: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

What do we do if there are 2 events?

Tuesday, February 9, 2010

Page 8: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

A coin is flipped twice

The first flip may be HEADOR

the first flip may be TAIL

The second flip may be HEAD

OR the second flip may be TAIL

THE COMPLETED TREE DIAGRAM SHOWS THERE ARE

4 POSSIBLE OUTCOMES

OUTCOME

H H

H T

T H

T T

HEAD

TAILHEAD

TAIL

HEAD

TAIL

Tuesday, February 9, 2010

Page 9: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

OUTFITS

YOU ARE CHOOSING AN OUTFIT FOR SCHOOL AND YOU ARE PICKING FROM A PILE OF 3 SHIRTS (RED, YELLOW, BLUE), 2 PAIRS OF PANTS (KHAKIS AND JEANS) AND 2 PAIRS OF SHOES (TENNIS SHOES, BOOTS).

Tuesday, February 9, 2010

Page 10: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

Shirt pants shoes outcomes

R

Y

BTB

TB

TB

TB

TB

TBK

J

K

J

K

J

R,K,TR,K,B

B,J,B

B,J,TB,K,BB,K,T

Y,J,BY,J,TY,K,BY,K,TR,J,BR,J,T

Tuesday, February 9, 2010

Page 11: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

You are at your school cafeteria that allows you to choose a lunch meal from a set menu. You have two choices for the Main course (a

hamburger or a pizza), Two choices of a drink (orange juice, apple juice) and Three choices of dessert (pie, ice cream, jello).

How many different meal combos can you select?_________ Lunch

Hamburger Pizza

Apple Orange

Pie Ice cream Jello

12 meals

Apple Orange

Pie Ice cream JelloPie Ice cream Jello Pie Ice cream Jello

Tuesday, February 9, 2010

Page 12: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

Sue has four pairs of shoes, five pairs of jeans, and seven sweaters. How many different clothing combinations can she select?

A useful technique to use when solving this question is to draw spaces to represent the number of events, and then writing the

number of ways each event can occur. The three events are shoes, jeans, and sweater:

and the number of ways each choice can be made is written in the space:

The total number of clothing combinations possible is:

Tuesday, February 9, 2010

Page 13: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

9 x 9 x 9 x 9 = 6561

9 x 8 x 7 x 6 = 3024

4 x 3 x 2 x 1 = 24

Tuesday, February 9, 2010

Page 14: Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A tree diagram is a way of ... Pie Ice cream Jello Pie Ice cream Jello Tuesday, February

Fundamental Counting Principle

• When two or more choices must be made together, the total number of outcomes can be determined without listing and counting them. The rule for this is known as "The Fundamental Counting Principle."

The Fundamental Counting Principle states the following: If one event can occur in 'a' ways, a second event in 'b' ways, a third event in 'c' ways, and so on, then the number of ways that all events can occur one after the other is the product a*b*c. . .

Tuesday, February 9, 2010


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