1. Sample Spaces, Subsets and Basic Probability
Assignment 2: Guided Notes

2. Warm-Up 1
If you have a standard dice what are the possibilities that you could roll?
If you flip a coin, what are the possibilities that you could flip?
Simplify:

3. Sample Space
Definition: A Sample Space is the set of all possible outcomes of an experiment.
Example: The sample space, S, of the days of the school week is
S = {Monday, Tuesday, Wednesday, Thursday, Friday}

4. Example 1 List the sample space, S, for each of the following:
Tossing a coin
Rolling a six-sided die
Drawing a marble from a bag that contains two red, three blue and one white marble

5. Example 1: Answers
List the sample space, S, for each of the following:
a. Tossing a coin
S = {Heads, Tails} or {H, T}
b. Rolling a six-sided die
S = {1,2,3,4,5,6}
c. Drawing a marble from a bag that contains two red, three blue and one white marble
S = {red, red, blue, blue, blue, white}

6. Intersections and Unions of Sets
The intersection of two sets (denoted A  B) is the set of all elements in both set A AND set B. (must be in both)
The union of two sets (denoted A  B) is the set of all elements in either set A OR set B. (everything)
Stress that intersection means AND and that union means OR

7. Ex 1 Example: Given the following sets, find A  B and A  B
A  B = {4, 7} (because 4 and 7 are the only number in BOTH)
A  B = {1, 2, 3, 4, 5, 6, 7, 8, 9}

8. Example 2 Given the following sets, find A  B and A  B
Stress that intersection means AND and that union means OR

9. Venn Diagrams
Sometimes drawing a diagram helps in finding intersections and unions of sets.
A Venn Diagram is a visual representation of sets and their relationships to each other using overlapping circles. Each circle represents a different set.

10. Example 3 What are the elements of set A?
Factors of 12
Factors of 16 1 2 4
8 16
What are the elements of set A?
What are the elements of set B?
Why are 1, 2, and 4 in both sets?
What is A  B?
What is A  B?

11. Example 3: Answers What are the elements of set A? {1,2,3,4,6,12}
Factors of 12
Factors of 16 1 2 4
8 16
What are the elements of set A?
{1,2,3,4,6,12}
What are the elements of set B?
{1,2,4,8,16}
Why are 1, 2, and 4 in both sets?
1,2 and 4 are factors of both 12 and 16

12. Example 3: Answers What is A  B? {1,2,4} What is A  B?
Factors of 12
Factors of 16 1 2 4
8 16
What is A  B?
{1,2,4}
What is A  B?
{1,2,3,4,6,8,12,16}

13. Example 4
In a freshman class of 60 students, 21 sign up for chorus, 29 sign up for band, and of those, 5 take both. 15 students in the class are not enrolled in either band or chorus.
Put this information into a Venn Diagram. If the sample space, S, is the set of all students in the class, let students in chorus be set A and students in band be set B.
What is A  B?
What is A  B?

14. S. A. B.

15. 16 5 Example 4: Answers A  B = {45} A  B = {5} 24
S. Students in the class
A. Students in Chorus
16 5
B. Students in Band 24
A  B = {45}
A  B = {5}

16. Complement of a set
The Complement of a set is the set of all elements NOT in the set.
The complement of a set, A, is denoted as AC
Ex: S = {…-3,-2,-1,0,1,2,3,4,…}
A = {…-2,0,2,4,…}
If A is a subset of S, what is AC?
Stress that compliment means NOT

17. Complement of a set
The Complement of a set is the set of all elements NOT in the set.
The complement of a set, A, is denoted as AC
Ex: S = {…-3,-2,-1,0,1,2,3,4,…} (all integers)
A = {…-2,0,2,4,…} (even numbers)
If A is a subset of S, what is AC?
AC = {-3,-1,1,3,5,…} (odds)
Stress that compliment means NOT

18. 16 5 Example 5: ANSWERS What is AC? 39 BC? 31 What is (A  B)C? 55
S. Students in the class
A. Students in Chorus
B. Students in Band 24
What is AC? 39 BC? 31
What is (A  B)C? 55
What is (A  B)C? 15

19. Practice