Probability I

1
Probability I
2
Sample space

• the collection of all possible outcomes of a
  chance experiment
• Roll a die S1,2,3,4,5,6

3
Event

• any collection of outcomes from the sample space
• Rolling a prime E 2,3,5
• Rolling a prime or even number E2,3,4,5,6

4
Complement

• Consists of all outcomes that are not in the
  event
• Not rolling a even
• EC1,3,5

5
Union

• the event A or B happening
• consists of all outcomes that are in at least one
  of the two events
• Rolling a prime or even number E2,3,4,5,6

6
Intersection

• the event A and B happening
• consists of all outcomes that are in both events
• Drawing a red card and a 2 E 2 hearts, 2
  diamonds

7
Mutually Exclusive (disjoint)

• two events have no outcomes in common
• Roll a 2 or a 5

8
Venn Diagrams

• Used to display relationships between events
• Helpful in calculating probabilities

9
Venn diagram - Complement of A
A
A
10
Venn diagram - A or B
A
B
11
Venn diagram - A and B
A
B
12
Venn diagram - disjoint events
A
B
13
Stat
Cal
Com Sci
Com Sci
Statistics Computer Science not Calculus
14
Cal
Stat
Com Sci
Calculus or Computer Science
15
Stat
Cal
Com Sci
(Statistics or Computer Science) and not Calculus
16
Cal
Stat
Com Sci
Statistics and not (Computer Science or Calculus)
17
Stat
Cal
105
30
20
10
10
20
80
Com Sci
Statistics or Computer Science?
170
18
Stat
Cal
105
30
20
10
10
20
80
Com Sci
20
Statistics and Computer Science?
19
Stat
Cal
105
30
20
10
20
10
80
Com Sci
Statistics or (Computer Science and Calculus)?
90
20
Stat
Cal
105
30
20
10
10
20
80
Com Sci
(Statistics or Computer Science) and Calculus?
50