Counting Methods - PowerPoint PPT Presentation

1 / 21
About This Presentation
Title:

Counting Methods

Description:

Represent all possible outcomes in compound events in an organized way (eg. ... SHOES: sandals, sneakers. How many total possible outfits do you have? The Tree Diagram ... – PowerPoint PPT presentation

Number of Views:47
Avg rating:3.0/5.0
Slides: 22
Provided by: mar8292
Category:

less

Transcript and Presenter's Notes

Title: Counting Methods


1
Counting Methods
  • Lesson 11-5

2
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.

3
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.

4
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

5
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
6
Using a tree diagram to find probability
1
2
3
4
5
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

7
P (pita with chicken)
1
P (pita with chicken)
8
Using a tree diagram to find probability
2
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!
9
Using a chart to find all possible outcomes
This chart is another way to show that there are
6 possible outcomes.
10
P (chicken) _________
P(chicken) 2/6 or 1/3
11
P (pita) _________
P(pita) 3/6 or 1/2
12
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?

13
The Tree Diagram
1
2
3
4
5
6
7
8
9
10
11
12
How many total possible outfits do you have? 12
14
P (blue shirt)
1
2
3
4
P (blue shirt) 4/12 or 1/3
15
P (blue jeans)
1
2
3
4
5
6
P (blue jeans) 6/12 or 1/2
16
P (sneakers)
1
2
3
4
5
6
P (sneakers) 6/12 or 1/2
17
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

18
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
19
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
20
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

21
3 x 2 6 types of jewelry
Write a Comment
User Comments (0)
About PowerShow.com