Counting Methods

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Counting Methods

• Lesson 11-5

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Math Standard SDAP 3.1

• Represent all possible outcomes in compound
  events in an organized way (eg. grids, tree
  diagrams) and express the theoretical probability
  of each outcome.

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Vocabulary Part 1

• Theoretical Probability
• How the outcomes SHOULD happen based upon the
  number of possible outcomes.
• This should prove true if the experiment is
  performed a very large number of times
• Experimental Probability
• How the outcomes ACTUALLY happen when you try it
  yourself.

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Tree Diagrams

• A way to represent theoretical probability
• A way to organize information in a chart/graph so
  that the observer can actually see what SHOULD
  happen

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Tree Diagram

• The cooking club has a sandwich luncheon. A
  sandwich consists of one type of bread and one
  choice of filling. How many types of sandwiches
  can be made?
• Breads pita or tortilla
• Fillings chicken, beef or vegetable

This is a tree diagram
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Using a tree diagram to find probability
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2
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6

• There are 6 choices, which means there are 6
  total possible outcomes
• Pita with chicken
• Pita with beef
• Pita with vegetable
• Tortilla with chicken
• Tortilla with beef
• Tortilla with vegetable

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P (pita with chicken)
1
P (pita with chicken)
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Using a tree diagram to find probability
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1
Based on this tree diagram, there are 6 different
types of sandwiches. Two of them are vegetable.
P (vegetable sandwich)
No matter how many layers you have, you ONLY
COUNT the items on the BOTTOM row!
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Using a chart to find all possible outcomes
This chart is another way to show that there are
6 possible outcomes.
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P (chicken) _________
P(chicken) 2/6 or 1/3
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P (pita) _________
P(pita) 3/6 or 1/2
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Create a tree diagram to show the following
information

• You are deciding what to wear to school in the
  morning. This is what you find in your closet
• TOPS blue T-shirt, red T-shirt, white T-shirt
• BOTTOMS blue jeans, shorts
• SHOES sandals, sneakers
• How many total possible outfits do you have?

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The Tree Diagram
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How many total possible outfits do you have? 12
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P (blue shirt)
1
2
3
4
P (blue shirt) 4/12 or 1/3
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P (blue jeans)
1
2
3
4
5
6
P (blue jeans) 6/12 or 1/2
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P (sneakers)
1
2
3
4
5
6
P (sneakers) 6/12 or 1/2
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The Counting Principle

• A quick mathematical way of finding the total
  possible outcomes.
• First, figure out what you have (look at the
  problem)
• Then multiply all the items together
• This helps with finding the total possible
  outcomes (how many things are on the bottom
  row)not the number of favorable outcomes

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The Counting Principle
To find the total possible outcomes, multiply
your number of choices together.

• 2 types of pasta
• Spaghetti
• Rigatoni
• 3 types of sauce
• Marinara
• Meat
• Alfredo

2 pasta 3 sauce
6 possible outcomes
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The Counting Principle
To find the total possible outcomes, multiply
your number of choices together.

• 12 colors
• 4 posters
• 3 sizes

12 4 3
144 possible outcomes
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Class Assignment
Juanita makes earrings, necklaces, and bracelets
from either beads or silver. How many kinds of
jewelry does she make?

• Find the number of total possible outcomes using
  all three of the following methods
• Tree diagram
• Table (chart)
• Counting principle

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3 x 2 6 types of jewelry