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 dieS={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 3.) Rolling 2 dice and counting the number of pips face up 4.) Toss a coin 5.) Toss a coin four times and record the results 6.) Toss a coin four times and record number of heads 7.) Flip a coin and roll a die

5.  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 # E C ={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. The shaded area represents the event A or B ( the union of two events). Union (or)

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) 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. 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 A, B & C are Disjoint A B C A B C A ∩ B ∩ C A υ B υ CA ∩ B ∩ C c

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

17. Calculus or Computer Science Stat Cal Com Sci

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

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

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

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

22. Stat Cal Com Sci Statistics or (Computer Science and Calculus)? 3020 105 10 20 80 10 90

23. Stat Cal Com Sci (Statistics or Computer Science) and Calculus? 3020 105 10 20 80 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