Definition: Random experiment Sample space How to make a Tree Diagram determine sample space Multiplication Principle

1. 1.4
Sets of Outcomes and Trees

2. Random Experiment
and Sample Space
 A random experiment is an experiment with
multiple possible outcomes.
Ex: Rolling a die, flipping a coin
 A “sample space” is the set of collection of all
those outcomes.
Ex: For experiment of “rolling a dice”,
SS = {1, 2, 3, 4, 5, 6}

3. Tree Diagram
 Tree Diagrams are a useful way to visually
represent a multi-stage experiment and
determine the sample space.

4. How to
make a Tree Diagram
 Let use this following experiment as the example for
our tree:
“There is Urn A and Urn B. Urn A has balls
numbered 1, 2, 3. Urn B has balls colored green and
red. You choose an urn and draw a ball from it.”
A B

5. Tree Diagram
The branches of a tree represent outcomes of a particular stage.
I personally like to line up the outcome from the same stage
vertically:

6.  Stage 1: Select the Urn
Stage 2: Pick the Ball
The resulting Sample Space is {Bg, Br, A1, A2, A3}, a total of 5 elements.

7. Representing an outcome twice
 A common mistake many students make is to put
down a repeated outcome multiple times. Let’s say
there are 2 green balls in urn B. You would still only
have one branch representing both green balls.
Making two separate branches for one outcome is
incorrect:
B

8. Quiz 1.4.1

9. Quiz 1.4.1
 Consider the following experiment: Fred goes to
dinner and have to pay the bill, which comes to
$7. He has one $10, one $5, and three $1. He
pull random bills out of the pocket until he has
enough to pay. How many elements are in the
sample space?
A. 9
B. 10
C. 11

10. Quiz 1.4.1
 Consider the following experiment: Fred goes to
dinner and have to pay the bill, which comes to
$7. He has one $10, one $5, and three $1. He
pull random bills out of the pocket until he has
enough to pay. How many elements are in the
sample space?
A. 9
B. 10
C. 11

11. Quiz 1.4.1
 Consider the following experiment: Fred goes to
dinner and have to pay the bill, which comes to
$7. He has one $10, one $5, and three $1. He
pull random bills out of the pocket until he has
enough to pay. How many elements are in the
sample space?
A. 9
B. 10
C. 11
 Answer: C

12. Multiplication principle
 If you have a multi-stage experiment, with equal number of
possibilities in each stage regardless of the previous stage,
there’s a simple way to calculate the number of element in
sample space.
 For example, Bob goes to McDonald to get a Happy meal. He
can choose cheeseburger, nuggets, or chicken sandwich for
entrée, soft drink, juice or milk for the drink, and 4 different
toys.
 The number of combinations he could get is 3 x 3 x 4 = 36.
(3 entrée, 3 drinks, 4 toys)

13. Quiz 1.4.2
 Mike goes to subway and gets a sandwich. He
can choose between 5 kinds of bread, 4 kinds of
cheese, and 3 kinds of meat. How many
different sandwiches does he have to choose
from?
A. 20
B. 60
C. 120

14. Quiz 1.4.2
 Mike goes to subway and gets a sandwich. He
can choose between 5 kinds of bread, 4 kinds of
cheese, and 3 kinds of meat. How many
different sandwiches does he have to choose
from?
A. 20
B. 60
C. 120
 Answer: B

15. Summary
 Definition:
 Random experiment
 Sample space
 How to make a Tree Diagram
 determine sample space
 Multiplication Principle

16.  Features
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 Over 116 practice problems with recorded solutions
 Discussion boards/homework help
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