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The probable is what usually happens. Aristotle Chapter 6: Probability
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Chance experiment: any activity or situation in which there is uncertainty about which outcome will result Fate laughs at probabilities. Bulwer, Lytton E.G.
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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
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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
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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}
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Venn Diagrams Used to display relationships between events Helpful in calculating probabilities
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Complement Consists of all outcomes that are not in the event –Not rolling a even # E C ={1,3,5}
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The rectangle represents the sample space and shaded area represents the event A. The shaded area represents the event not A.
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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}
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The shaded area represents the event A or B ( the union of two events). Union (or)
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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}
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Intersection (and) The shaded area represents the event A and B (the intersection of two sets).
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Mutually Exclusive (disjoint) two events have no outcomes in common –Roll a “2” or a “5”
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Two events that have no common outcomes are said to be disjoint or mutually exclusive. A and B are disjoint events
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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
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Com Sci Statistics & Computer Science & not Calculus StatCal Com Sci
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Calculus or Computer Science Stat Cal Com Sci
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(Statistics or Computer Science) and not Calculus StatCal Com Sci
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Statistics and not (Computer Science or Calculus) Stat Cal Com Sci
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Stat Cal Com Sci Statistics or Computer Science? 30 105 20 10 20 80 170
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Stat Cal Com Sci Statistics and Computer Science? 30 105 20 10 20 80 20
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Stat Cal Com Sci Statistics or (Computer Science and Calculus)? 3020 105 10 20 80 10 90
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Stat Cal Com Sci (Statistics or Computer Science) and Calculus? 3020 105 10 20 80 50
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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
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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?
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Always be a little improbable. Wilde, Oscar
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