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UNIT 7 LESSON 1: PROBABILITY & TREE DIAGRAMS, Summaries of Probability and Statistics

Create a tree diagram. Find the total number of possible outcomes and list them. Page 3. CLASSIC PROBABILITY.

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UNIT 7 LESSON 1: PROBABILITY & TREE DIAGRAMS
NOTES
Experiment
A process used to obtain observations
Examples: flipping a coin to observe if its heads, Rolling a die to see what number is
on top, drawing a card from a deck to see if it is a heart
Outcome
A particular result of an experiment
Examples: Rolling a die the outcome could be a 4
Drawing a heart from a deck could be an Ace
Sample Space
the set of all possible outcomes of an experiment
Examples: Rolling a die the sample space is {1,2,3,4,5,6}
Drawing a heart from a deck {A, 2,3,4,5,6,7,8,9,10,J,Q,K}
Event
A subset of the sample space of an experiment
Examples: Rolling a die {2,3,4} is a subset of the sample space {1,2,3,4,5,6}
Drawing a heart {A,K,Q,J} is a subset of {A, 2,3,4,5,6,7,8,9,10,J,Q,K}
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UNIT 7 LESSON 1: PROBABILITY & TREE DIAGRAMS

NOTES

Experiment

 A process used to obtain observations

 Examples: flipping a coin to observe if its heads, Rolling a die to see what number is on top, drawing a card from a deck to see if it is a heart

Outcome

 A particular result of an experiment

 Examples: Rolling a die the outcome could be a 4 Drawing a heart from a deck could be an Ace

Sample Space

 the set of all possible outcomes of an experiment

 Examples: Rolling a die the sample space is {1,2,3,4,5,6} Drawing a heart from a deck {A, 2,3,4,5,6,7,8,9,10,J,Q,K}

Event

 A subset of the sample space of an experiment

 Examples: Rolling a die {2,3,4} is a subset of the sample space {1,2,3,4,5,6} Drawing a heart {A,K,Q,J} is a subset of {A, 2,3,4,5,6,7,8,9,10,J,Q,K}

FUNDAMENTAL COUNTING PRINCIPAL OR THE MULTIPLICATION PRINCIPLE

If one event has m possible outcomes and a second independent event has n possible outcomes, then there is m x n total possible outcomes for the two events together.

EXAMPLE 1: Brian must dress up for his job interview. He has three dress shirts, two ties, and two pairs of dress pants. How many possible outfits does he have?

EXAMPLE 2: A restaurant serves 5 main dishes, 3 salads, and 4 desserts. How many different meals can be ordered if each has a main dish, a salad, and a dessert?

TREE DIAGRAM

A visual display of the total number of outcomes of an experiment consisting of a series of events

Using a tree diagram, you can determine the total number of outcomes and individual outcomes

EXAMPLE 3: You are going to Taco Bell for dinner. You can either get a crunchy or a soft taco. You can choose either beef, chicken, or fish. Create a tree diagram. Find the total number of possible outcomes and list them.

USING A TREE DIAGRAM AND THE FUNDAMENTAL COUNTING

PRINCIPLE TO FIND THE PROBABILITY

*When using a tree diagram to find the probability of a certain outcome,

multiply across the branches.

EXAMPLE 7:

What is the probability of getting a crunchy chicken taco?

EXAMPLE 8: An Italian restaurant sells small, medium, and large pizzas. You can choose either pan or hand tossed crust. There are three toppings to choose from: pepperoni, sausage, and extra cheese. Draw a tree diagram to find the probability of ordering a medium, pan, pepperoni pizza?

NAME ____________________________________ DATE ____________

PRACTICE:

Draw a tree diagram for each of the problems.

NAME ________________________________________ DATE ___________

PRACTICE #2: USING TREE DIAGRAMS TO FIND OUTCOMES AND

PROBABILITIES