Tree Diagrams - Mrs. Poland's Math · Mrs. Poland September 21, 2009 Tuesday, February 9, 2010. A...
Transcript of 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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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
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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
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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
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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)
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Similarly, the tree diagram for flipping a coin is
Tails
Heads
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What do we do if there are 2 events?
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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
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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).
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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
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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
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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:
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9 x 9 x 9 x 9 = 6561
9 x 8 x 7 x 6 = 3024
4 x 3 x 2 x 1 = 24
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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. . .
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