Download Lesson 5.4 Tree Diagram Notes

Lesson 5.4 Tree Diagram Notes
Statistics
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Multiplication Rule of Counting
The total possible outcomes are found by multiplying the options.
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 dessert?
Example 3: How many license plate numbers consisting of three letters followed by three numbers
are possible when repetition is allowed?
Example 4: How many license plate numbers consisting of three letters followed by three numbers
are possible when repetition is NOT allowed?
Using Tree Diagrams
 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 5: Jacqueline is in a nursing program and is required to take a course in psychology
and one in physiology (A and P) next semester. She also wants to take Spanish II.
According to the course catalogue, there are two sections of psychology, two of A and P,
and three of Spanish II.
a. How many different class schedules can Jacqueline choose from? (Assume that there
are no conflicts.)
b. Make a tree diagram that shows all the possible course schedules for Jacqueline.
Lesson 5.4 Tree Diagram Notes
Statistics
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Example 6: There are two archers: Li has a ¾ probability of hitting a target and Yukka has a
4/5 probability of hitting the target.
a. Draw a tree diagram.
If they both shoot simultaneously, what is the probability that:
b. they will both hit the target
c. that Li will hit and Yukka will miss
d. that Yukka will hit and Li will miss
e. they will both miss the target.
Example 6: Carl is not having much luck lately. His car will only start 80% of the time and
his motorbike will only start 60% of the time.
a. draw a tree diagram of the situation
b. using that tree diagram, what is the probability that:
i.
both will start
ii.
Carl has no choice but to use his car.
Lesson 5.4 Tree Diagram Notes
Statistics
Page 3 of 3
Example 7: Bag A contains 3 red and 2 yellow tickets. Bag B contains 1 red and 4 yellow
tickets. A bag is randomly selected by tossing a coin and one ticket is removed.
a. Draw a tree diagram.
b. Determine the probability that it is yellow.
Example 8: Suppose there are five balls in a bowl. They are identical except for color.
Three are red and two are blue. You are instructed to draw out one ball, not the color, and
set it aside. Then you are to draw out another ball and note its color.
a. Draw a tree diagram to represent the outcomes.
b. How many outcomes are possible?
c. What is the probability of each outcome?
Assignment: p. 180 #2, 3, 7, 9; p. 192 #2, 5, 7, 8, 9, 10, 12