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Probability I

Probability I. Sample space. the collection of all possible outcomes of a chance experiment Roll a die S={1,2,3,4,5,6}. Event. any collection of outcomes from the sample space Rolling a prime # E= {2,3,5} Rolling a prime # or even number E={2,3,4,5,6}.

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Probability I

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  1. Probability I

  2. Sample space the collection of all possible outcomes of a chance experiment Roll a die S={1,2,3,4,5,6}

  3. Event • any collection of outcomes from the sample space • Rolling a prime # E= {2,3,5} • Rolling a prime # or even number E={2,3,4,5,6}

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

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

  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 A B

  11. Venn diagram - A and B A B

  12. Venn diagram - disjoint events A B

  13. Stat Cal Com Sci Com Sci Statistics & Computer Science & not Calculus

  14. Cal Stat Com Sci Calculus or Computer Science

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

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

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

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

  19. Stat Cal 105 30 20 10 20 10 80 Com Sci Statistics or (Computer Science and Calculus)? 90

  20. Stat Cal 105 30 20 10 10 20 80 Com Sci (Statistics or Computer Science) and Calculus? 50

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