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THE MATHEMATICAL STUDY OF RANDOMNESS. SAMPLE SPACE the collection of all possible outcomes of a chance experiment  Roll a dieS={1,2,3,4,5,6}

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Presentation on theme: "THE MATHEMATICAL STUDY OF RANDOMNESS. SAMPLE SPACE the collection of all possible outcomes of a chance experiment  Roll a dieS={1,2,3,4,5,6}"— Presentation transcript:

1 THE MATHEMATICAL STUDY OF RANDOMNESS

2 SAMPLE SPACE the collection of all possible outcomes of a chance experiment  Roll a dieS={1,2,3,4,5,6}

3 EVENT any collection of outcomes from the sample space  Rolling a prime #E= {2,3,5}

4 COMPLEMENT Consists of all outcomes that are not in the event  Not rolling a even # E C ={1,3,5}

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

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 AB

11 VENN DIAGRAM - A AND B A B

12 VENN DIAGRAM - DISJOINT EVENTS A B

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

14 Calculus or Computer Science Stat Cal Com Sci

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

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

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

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

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

20 Stat Cal Com Sci (Statistics or Computer Science) and Calculus? 3020 105 10 20 80 50


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