document.write( "Question 1041972: To gather data involving their classmates, 34 fourth graders each filled out a personal information survey sheet. In the category of pets, 16 students had a cat, 21 students had a dog, and 8 students had both a dog and a cat. If a student is randomly selected from this class, what is the probability the student will have a dog or a cat? \n" ); document.write( "
Algebra.Com's Answer #656951 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
You can do it like the other tutor told you, but I think
\n" ); document.write( "you are supposed to either \r
\n" ); document.write( "\n" ); document.write( "1. be learning the formula:
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\n" ); document.write( "P(A or B) = P(A) + P(B) - P(A and B)
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\n" ); document.write( "P(cat or dog) = P(cat) + P(dog) - P(cat and dog)\r
\n" ); document.write( "\n" ); document.write( "P(cat or dog) = 16/34 + 21/34 - 8/34\r
\n" ); document.write( "\n" ); document.write( "P(cat or dog) = 29/34\r
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\n" ); document.write( "\n" ); document.write( "2. learning to use Venn diagrams (sometimes they are
\n" ); document.write( "called Euler diagrams). So let's do it that way too:\r
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\n" ); document.write( "\n" ); document.write( "Everybody within the red circle has a cat.
\n" ); document.write( "Everybody within the blue circle has a dog.
\n" ); document.write( "Those in the overlapping part of the circles have
\n" ); document.write( "both a cat and a dog.
\n" ); document.write( "Those outside both circles have neither a cat not a dog.
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\n" ); document.write( "8 students had both a dog and a cat.
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document.write( "So we put 8 in the middle, the part where the circles\r\n" );
document.write( "overlap.\r\n" );
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\n" ); document.write( "16 students had a cat
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document.write( "Those 16 include the 8 that have both a cat and a dog,\r\n" );
document.write( "as well as those who have only a cat.  We already have\r\n" );
document.write( "put those 8 with both cat and dog in the part of the\r\n" );
document.write( "red circle that overlaps the blue circle, so to find\r\n" );
document.write( "out how many have a cat only, we subtract the 8 in the\r\n" );
document.write( "overlapping part from the 16, getting 8 that have a cat \r\n" );
document.write( "only.  So we put 8 in the left part of the red circle, \r\n" );
document.write( "to indicate that 8 people have a cat ONLY, and no dog. \r\n" );
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\n" ); document.write( "21 students had a dog
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document.write( "Those 21 include the 8 that have both a dog and a cat,\r\n" );
document.write( "as well as those who have only a dog.  We already have\r\n" );
document.write( "put those 8 with both dog and cat in the part of the\r\n" );
document.write( "red circle that overlaps the blue circle, so to find\r\n" );
document.write( "out how many have a dog only, we subtract the 8 in the\r\n" );
document.write( "overlapping part from the 21, getting 13 that have a dog \r\n" );
document.write( "only.  So we put 13 in the right part of the blue circle, \r\n" );
document.write( "to indicate that 13 people have a dog ONLY, and no cat. \r\n" );
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document.write( "Now we have 8 in the \"cat only\" category, the left part of the\r\n" );
document.write( "red circle, 8 in the \"cat and dog\" category, and 13 in the\r\n" );
document.write( "\"dog only\" category.  But that's only 8+8+13=29 students that\r\n" );
document.write( "have either a cat or a dog or both.  There are 34 students in \r\n" );
document.write( "all. So that leaves 34-29=5 students that have neither a cat \r\n" );
document.write( "nor a dog.  So we put 5 outside both circles:\r\n" );
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document.write( "So the probability that a student has either a cat or a dog\r\n" );
document.write( "is the probability that he is in one of the 8+8+13 = 29 in\r\n" );
document.write( "the circles, which is 29/34.\r\n" );
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document.write( "Edwin
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