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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
