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Unformatted text preview: Math 62–Probability & Statistics Summer 2004 Homework 1 Solutions 3. Consider a universal set consisting of the integers 1 through 10, or U = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } . Let A = { 2 , 3 , 4 } , B = { 3 , 4 , 5 } , and C = { 5 , 6 , 7 } . By enumeration, list the membership of the following sets. (c) A ∩ B . If we simplify this using De Morgan’s Law, we have A ∩ B = A ∪ B = { 2 , 3 , 4 } ∪ { 3 , 4 , 5 } = { 2 , 3 , 4 , 5 } . (e) A ∩ ( B ∪ C ). This one is easier to do directly: A ∩ ( B ∪ C ) = { 2 , 3 , 4 } ∩ ( { 3 , 4 , 5 } ∪ { 5 , 6 , 7 } ) = { 2 , 3 , 4 } ∩ { 3 , 4 , 5 , 6 , 7 } = { 3 , 4 } = { 1 , 2 , 5 , 6 , 7 , 8 , 9 , 10 } . 7. Diodes from a batch are tested one at a time and marked either defective or nondefective. This is continued until either two defective items are found or five items have been tested. Describe the sample space for this experiment. If D and N represent defective and nondefective diodes respectively, then we can enumerate the sample space as S = { DD,DND,DNND,DNNND,DNNNN,NDD,NDND,NDNND,NDNNN,NNDD,NNDND, NNDNN,NNNDD,NNNDN,NNNND,NNNNN } ....
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 Spring '11
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