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

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

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

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}

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}

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

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

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

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}

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

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}

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

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

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

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

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

Calculus or Computer Science Stat Com Sci Calculus or Computer Science

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

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

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

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

90 Statistics or (Computer Science and Calculus)? Stat Cal 105 30 20 80 Com Sci Statistics or (Computer Science and Calculus)? 90

50 (Statistics or Computer Science) and Calculus? Stat Cal 105 30 20 80 Com Sci (Statistics or Computer Science) and Calculus? 50

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

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?

Always be a little improbable. Wilde, Oscar