March 03, 2017
March 03, 2017
(13.1) Representing Sample Spaces
Objective: To use lists, tables, and tree diagrams to represent sample spaces.
To use the Fundamental Counting Principle to count outcomes.
Why: This will allow us to determine probabilities of events.
March 03, 2017
(13.1) Obj:
Definitions:
To use lists, tables, and tree diagrams to represent sample spaces.
To use the Fundamental Counting Principle to count outcomes.
Experiment: a situation involving chance that leads to results called outcomes
Outcome: the result of a single performance or trial of an experiment
Event: one or more outcomes of an experiment
Example 1:
In a football game, a referee tosses a fair coin to determine which team will
take possession of the football first. The coin can land on heads or tails.
Identify the following:
experiment:
possible outcomes:
an event:
March 03, 2017
Obj: To use lists, tables, and tree diagrams to represent sample spaces.
To use the Fundamental Counting Principle to count outcomes.
Sample Space: the set of all possible outcomes. A sample space can be
represented by using an organized list, a table, or a tree diagram.
Example 2:
One red token and one black token are placed in a bag. A token is drawn and
the color is recorded. It is then returned to the bag and a second draw is made.
Represent the sample space for this experiment by making an organized list, a
table, and a tree diagram.
Organized List:
Table:
Tree Diagram:
March 03, 2017
Obj: To use lists, tables, and tree diagrams to represent sample spaces.
To use the Fundamental Counting Principle to count outcomes.
Two-stage Experiment: experiment with two stages.
Multi-stage Experiments: experiments with more than two stages.
March 03, 2017
Obj: To use lists, tables, and tree diagrams to represent sample spaces.
To use the Fundamental Counting Principle to count outcomes.
Example 3: (Chef's Salad)
A chef's salad at a local restaurant comes with a choice of French, ranch, or
blue cheese dressings and optional toppings of cheese, turkey, and eggs.
Draw a tree diagram to represent the sample space for salad orders.
March 03, 2017
Obj: To use lists, tables, and tree diagrams to represent sample spaces.
To use the Fundamental Counting Principle to count outcomes.
Fundamental Counting Principle:
Method to find the number of possible outcomes in some two-stage or multi-stage
experiments.
The number of possible outcomes in a sample space can be found by multiplying
the number of possible outcomes from each stage or event.
In a k-stage experiment, let
n1 = the number of possible outcomes for the first stage
n2 = the number of possible outcomes for the second stage
nk = the number of possible outcomes for the kth stage after the first k-1 stages
have occured
Then the total possible outcomes for this k-stage experiment is
n1 n2 n3 ... nk
March 03, 2017
Obj: To use lists, tables, and tree diagrams to represent sample spaces.
Example 4: (Cars)
To use the Fundamental Counting Principle to count outcomes.
New cars are available with a wide selection of options for the consumer.
One option is chosen from each category shown. How many different cars
could a consumer create in the chosen make and model?
March 03, 2017
Obj: To use lists, tables, and tree diagrams to represent sample spaces.
To use the Fundamental Counting Principle to count outcomes.
Examples:
Find the number of possible outcomes for each situation.
1. The answer sheet shown is completed.
46 24
2. A die is rolled four times.
3. A pair of women's shoes come in whole sizes from 5 through 11 in red, navy,
brown, or black. They can be leather or suede and are available in three
different widths.
March 03, 2017
March 03, 2017
Obj: To use lists, tables, and tree diagrams to represent sample spaces.
To use the Fundamental Counting Principle to count outcomes.
HF:
(HR) (13.1) Pg.918: 7-17odd, 22-24