MATH 1071 VennDiagrams_11:14

# There were 250 responses with the following results

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Unformatted text preview: 5 were interested in an interview show and a documentary, but not reruns. 10 were interested in an interview show and reruns, but not a documentary. 35 were interested in reruns, but not an interview show. 60 were interested is an interview, but not a documentary. 25 were interested in a documentary and reruns. 15 were interested in an interview show and reruns. 20 were interested in none of the three. How many are interested in exactly one kind of show? Patrick Newberry Venn Diagrams Cardinality 10 / 14 Examples Notes n(U ) = 250 blue squares describe the 3 numbers that meet the question being answered I0 D I Total R 5 20 25 R0 75 55 130 Total 80 75 155 n(D \ I \ R 0 ) = 75 n(D 0 \ I \ R ) = 10 n(I 0 \ R ) = 35 n(D 0 \ I ) = 60 D0 I I 0 Total R 10 15 25 R0 50 20 70 Total 60 35 95 n(D \ R ) = 25 n(I \ R ) = 15 n(D 0 \ I 0 \ R 0 ) = 20 n (D \ I 0 \ R 0 ) Total I I0 Total R 15 35 50 R0 125 75 200 Total 140 110 250 + n (D 0 \ I \ R 0 ) + n (D 0 \ I 0 \ R ) = 120 Patrick Newberry November 14, 2012 Venn Diagrams November 14, 2012 11 / 14 Cardinality Examples A survey of 220 families showed that Notes 83 had a dog. 64 had a cat. 28 had a dog and a cat. 84 had neither a cat nor a dog, and in addition did not have a parak...
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