01 Venn - Axioms

01 Venn - Axioms - Summary Examples Example 1 An experiment...

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1/5/10 Summary Examples Example 1 An experiment consists of tossing a die and then flipping a coin once if the die outcome is even. If the die outcome is odd, the coin is flipped twice. o Describe the sample space by listing its elements. o Describe the sample space using a tree diagram. Answer: S = {(1HH), (1HT), (1TH), (1TT), (2H), (2T), (3HH), (3HT), (3TH), (3TT), (4H), (4T), (5HH), (5HT), (5TH), (5TT), (6H), (6T)} 1 2 3 4 5 6 H T H T H T H T H T H T H T H T H T H T H T H T
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1/5/10 Summary Examples Example 2 For the sample in example 1: list the elements of event A: a number less than 3 occurs on the die A = {(1HH), (1HT), (1TH), (1TT), (2H), (2T)} list the elements of event B: two tails occur B = {(1TT), (3TT), (5TT)} list the elements of event A& A& = {(3HH), (3HT), (3TH), (3TT), (4H), (4T), (5HH), (5HT), (5TH), (5TT), (6H), (6T)} list the elements of event A&&B A ±B = {(3TT), (5TT)} list the elements of event A&B
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1/5/10 Summary Examples Example 3 Let S = {x|0<x<12} M = {x|1<x<9} and N= {x| 0<x<5}. Find: (What is x? real number? Integer? DOES IT MATTER?)
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01 Venn - Axioms - Summary Examples Example 1 An experiment...

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