1. Addition Rule Example-Not mutually exclusive events
AM: Applied Mechanics; Chem: Chemistry; Comp: Computer 5
Chem
Venn Diagram
Total 120 x AM 25 15 10 y
Comp 20 30

2. Example-Not mutually exclusive events
AM: Applied Mechanics; Chem: Chemistry; Comp: Computer AM
Comp 30 15 5 20 y
Chem 10 x 25
Venn Diagram
Total 120
How many of the students take Applied Mechanics
and Chemistry but not Computers?
A total of 45 of them take chemistry, then
x =45 → x=5

3. Example-Not mutually exclusive events
AM: Applied Mechanics; Chem: Chemistry; Comp: Computer AM
Comp 30 15 5 20 y
Chem 10 x 25
Venn Diagram
Total 120
b. How many of the students take only Computers?
y=120 → y =10

4. Example-Not mutually exclusive events
AM: Applied Mechanics; Chem: Chemistry; Comp: Computer AM
Comp 30 15 5 20 y
Chem 10 x 25
Venn Diagram
Total 120
c. What is the total number of the students taking Computers?
y= =65

5. Example-Not mutually exclusive events
AM: Applied Mechanics; Chem: Chemistry; Comp: Computer AM
Comp 30 15 5 20 y
Chem 10 x 25
Venn Diagram
Total 120
If a student is chosen at random from those who take neither Chemistry
nor Computers, what is the probability that he or she does not take
Applied Mechanics either?
The number of students take neither Chemistry not Computers: 30+15=45; The number of students do not take AM, Chem and Comp: 30;
then the probability that he or she does not take AM is 30/45=2/3.

6. Example-Not mutually exclusive events
AM: Applied Mechanics; Chem: Chemistry; Comp: Computer AM
Comp 30 15 5 20 y
Chem 10 x 25
Venn Diagram
Total 120
e. If one of the students who take at least two of the three courses is chosen
at random, what is the probability that he or she takes all three courses?
The number of students take at least two of the three courses: x =60
The number of students take all three courses: 10 (yellow)
Then the probability that he or she takes all three courses is 10/60=1/6