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Chapter 6 Section 2

Chapter 6 Section 2. Experiments, Outcomes, and Events. Basic Definitions. Experiment: An activity with an observable outcome. Trial: The act of performing a single experiment. Outcome: The observable result of the experiment. Sample Space (S). Sample Space:

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Chapter 6 Section 2

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  1. Chapter 6 Section 2 Experiments, Outcomes, and Events

  2. Basic Definitions • Experiment: An activity with an observable outcome. • Trial: The act of performing a single experiment. • Outcome: The observable result of the experiment.

  3. Sample Space (S) • Sample Space: • The set of all possible outcomes of the experiment. • Set should be chosen so that there is no overlap • S = { ‘list of all possible outcomes’ } • You can think of the sample space as the universal set for the experiments.

  4. Events • Event: A set that is a subset of the sample space. • Impossible Event: An event that cannot occur. • i.e. The outcome is not in the sample space. • Denoted using the symbol: Ø

  5. Exercise 5 (page 270) • Situation: Two urns, each containing several balls. Both urns contain some red balls and some white balls. ? ? ? ? ? ? ? ? ? ? ? ? Urn I Urn II

  6. Exercise 5 Notation Definition Let : • I represent Urn I • II represent Urn II • R represent a Red Ball • W represent a White Ball Experiment: Pick one of the two urns and then draw a ball from the urn that is picked.

  7. Exercise 5 Part (a) • What is a suitable sample space for this experiment? • Possible Solution: S = { ( I , R ) , ( I , W ) , ( II , R ) , ( II , W) }

  8. Exercise 5 Part (b) • Describe the event “Urn I is selected” E = { ( I , R ) , ( I , W ) }

  9. For events E and F • The event E  F occurs precisely when either event E or event F (or both) occur. • The event E  F occurs precisely when both events E and event F occur.

  10. Other relationships: • Event E occurs when event E does not occur. • E  E = S • E  E =  • Two events are mutually exclusive (or disjoint) events when: E  F = 

  11. Exercise 7 (page 270) • Efficiency expert records the time that it takes an assembly line worker to perform a particular task. • Let event… E = { more than five minutes } F = { less than eight minutes } G = { less than four minutes }

  12. Exercise 7 (part a) • Describe the sample space for this experiment. S = { all positive numbers of minutes }

  13. Exercise 7 (part b) Describe the following: • E  F E  F = { more than 5 minutes but less than 8 minutes } • E  G E  G =  • E  E  = { 5 minutes or less }

  14. Exercise 7 (part b) continued Describe the following: 4. E  F E  F = {5 minutes or less } 5. E  F  G E  F  G = { less than 4 minutes } 6. E  F E  F = S

  15. Exercise 17 (page 271) • Toss a coin 10 times and observe the number of heads. • Sample space? S = { 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } • Describe the event E of “more than 5 heads” in terms of the sample space. E = { 6 , 7 , 8 , 9 , 10 }

  16. Exercise 3(page 270) Toss a coin twice and observe the sequence of heads (H) and tails (T). • Define the sample space: S = { HH , HT , TH , TT } • The first toss is a head: E = { HH , HT}

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