1. The probable is what usually happens. Aristotle
Chapter 6: Probability

2. Chance experiment: any activity or situation in which there is uncertainty about which outcome will result
Fate laughs at probabilities.
Bulwer, Lytton E.G.

3. Sample Space: collection of all possible outcomes of a chance experiment
Roll a die S={1,2,3,4,5,6}
Probability is the very guide of life.
Cicero

4. What is the sample space?
1.) Rolling 1 die
2.) Rolling 2 dice and counting the number of pips face up
3.) Toss a coin
4.) Toss a coin three times and record the results
5.) Flip a coin and roll a die
S = {1,2,3,4,5,6}
S = {2,3,4,5,6,7,8,9,10,11,12}
S = {H,T}
S = {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}
S = {H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6}

5. A simple event is an event consisting of exactly one outcome.
An event is any collection of outcomes from the sample space of a chance experiment.
Rolling a prime # E = {2,3,5}
A simple event is an event consisting of exactly one outcome.
Rolling a 6: E = {6}

6. Venn Diagrams Used to display relationships between events
Helpful in calculating probabilities

7. Complement Consists of all outcomes that are not in the event
Not rolling a even #
EC={1,3,5}

8. The rectangle represents the sample space and shaded area represents the event A.
The shaded area represents the event not A.

9. 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 E={2,3,4,5,6}

10. Union (or) A or B ( the union of two events).
The shaded area represents the event
A or B ( the union of two events).

11. 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}

12. Intersection (and) A and B (the intersection of two sets).
The shaded area represents the event
A and B (the intersection of two sets).

13. Mutually Exclusive (disjoint)
two events have no outcomes in common
Roll a “2” or a “5”

14. A and B are disjoint events
Two events that have no common outcomes are said to be disjoint or mutually exclusive.
A and B are disjoint events

15. Some illustrations A B C A, B & C are Disjoint A B C A ∩ B ∩ C A B C A
A ∩ B ∩ Cc

16. Statistics & Computer Science & not Calculus
Com Sci
Com Sci
Statistics & Computer Science & not Calculus

17. Calculus or Computer Science
Stat
Com Sci
Calculus or Computer Science

18. (Statistics or Computer Science) and not Calculus
Com Sci
(Statistics or Computer Science) and not Calculus

19. Statistics and not (Computer Science or Calculus)
Com Sci
Statistics and not (Computer Science or Calculus)

20. 170 Statistics or Computer Science? Stat Cal 105 30 20 10 10 20 80
Com Sci
Statistics or Computer Science?
170

21. 20 Statistics and Computer Science? Stat Cal 105 30 20 10 10 20 80
Com Sci 20
Statistics and Computer Science?

22. 90 Statistics or (Computer Science and Calculus)? Stat Cal 105 30 2080
Com Sci
Statistics or (Computer Science and Calculus)? 90

23. 50 (Statistics or Computer Science) and Calculus? Stat Cal 105 30 2080
Com Sci
(Statistics or Computer Science) and Calculus? 50

24. Country-Western songs emphasize three basic themes: love, prison, and trucks. A survey of the local Country-Western radio station produced the following data:
12 songs about a truck driver who is in love while in prison
2 about people in prison who are not in love and do not drive trucks
8 about people who are out of prison, are not in love, and do not drive a truck
13 about a prisoner in love
28 about a person in love
18 about a truck driver in love
16 about truck drivers who are not in prison
3 about a truck driver in prison who is not in love

25. 12 songs about a truck driver who is in love while in prison
2 about people in prison who are not in love and do not drive trucks
8 about people who are out of prison, are not in love, and do not drive a truck
13 about a prisoner in love
28 about a person in love
18 about a truck driver in love
16 about truck drivers who are not in prison
3 about a truck driver in prison who is not in love
How many songs were about:
a.) truck drivers?
b.) prisoners?
c.) truck drivers in prison?
d.) people not in prison?
e.) people not in love?
f.) How many songs were surveyed?

26. Always be a little improbable.
Wilde, Oscar