TAMU MATH 141  14107cn71 (6 pages)
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Lecture Notes
 Pages:
 6
 School:
 Texas A&M University
 Course:
 Math 141  Business Math I
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c Kendra Kilmer October 4 2007 Section 7 1 Experiments Sample Spaces and Events Definition An experiment is an activity with an observable result Definition The outcome is the result of an experiment Definition The sample space is the set of all outcomes of an experiment Definition An event is a subset of the sample space Note An event E is said to occur whenever E contains the observed outcome Definition E and F are mutually exclusive if E F Note All of the set operations union intersection complement work the same with events Example 1 Let s consider the experiment of rolling a fair six sided die and observing the number that lands uppermost a Determine the sample space b Find the event E where E x x is an even number c Find the event F where F x x is a number greater than 2 d Find the event E F e Find the event E F f Are the events E and F mutually exclusive g Are the events E and F complementary Example 2 Let s consider the experiment of flipping a fair coin two times and observing the resulting sequence of heads and tails a Determine the sample space b Find the event E where E x x has one or more heads c Find the event F where F x x has more than 2 heads d List all events of this experiment 1 c Kendra Kilmer October 4 2007 Example 3 An experiment consists of most on each die 1 1 1 2 1 3 S 1 4 1 5 1 6 casting a pair of dice and observing the number that falls upper 2 1 2 2 2 3 2 4 2 5 2 6 3 1 3 2 3 3 3 4 3 5 3 6 4 1 4 2 4 3 4 4 4 5 4 6 5 1 5 2 5 3 5 4 5 5 5 6 6 1 6 2 6 3 6 4 6 5 6 6 a Determine the event that the sum of the numbers falling uppermost is less than or equal to 6 b Determine the event that the number falling uppermost on one die is a 4 and the number falling uppermost on the other die is greater than 4 Example 4 The manager of a local bank observes how long it takes a customer to complete his transactions at the ATM a Describe an appropriate sample space for this experiment b Describe the event that it takes a customer between 2 and 3 minutes
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