document.write( "Question 956675: In a class of 160 students, 90 are taking math, 78 are taking science, and 62 are taking both math and science. What is the probability of randomly choosing a student who is not taking science?
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Algebra.Com's Answer #584500 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!

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document.write( "All the math students are in the red circle, labeled M for math.\r\n" );
document.write( "All the science students are in the blue circle, labeled S for science.\r\n" );
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document.write( "Some are in both circles, and some are in neither circle.\r\n" );
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document.write( "The letter a represents the students who are in the red circle but not\r\n" );
document.write( "in the blue circle. So a = the number of students taking math but not\r\n" );
document.write( "taking science.\r\n" );
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document.write( "The letter c represents the students who are in the blue circle but not\r\n" );
document.write( "in the red circle. So c = the number of students taking science but not\r\n" );
document.write( "taking math.\r\n" );
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document.write( "The letter b represents the students who are in both the red circle and\r\n" );
document.write( "also in the red circle. So b = the number of students taking both math\r\n" );
document.write( "and science.\r\n" );
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document.write( "The letter d represents the students who are not in either circle. So b=\r\n" );
document.write( "the number of students not taking math or science.\r\n" );
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document.write( "We look at the clue that is the most conclusive first,\r\n" );
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\n" ); document.write( "62 are taking both math and science.
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document.write( "So we knoe that b=62, so we write b=62 and put that in the middle\r\n" );
document.write( "region:\r\n" );
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document.write( "Next we look at the clue that reads:\r\n" );
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\n" ); document.write( " 90 are taking math,
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document.write( "That means that there are 90 students altogether in the red circle. We already\r\n" );
document.write( "have b=62 in the right part of the red circle, so there must be 90-62 or 28\r\n" );
document.write( "in the left part of the red circle, so a=28, and we write that in the left\r\n" );
document.write( "part of the red circle:\r\n" );
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document.write( "Next we look at the clue that reads:\r\n" );
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document.write( "That means that there are 78 students altogether in the blue circle. We already\r\n" );
document.write( "have b=62 in the left part of the blue circle, so there must be 78-62 or 16\r\n" );
document.write( "in the right part of the blue circle, so c=16, and we write that in the right\r\n" );
document.write( "part of the blue circle:\r\n" );
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document.write( "Next we look at the remaining clue that reads:\r\n" );
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\n" ); document.write( " a class of 160 students
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document.write( "We have accounted for a=28, b=62, and c=16 or 28+62+16 or 106 of the\r\n" );
document.write( "160, so there are 160-106 or 54 remaining students who are not in \r\n" );
document.write( "either of the two circles, so d=54.  So we write d=54 in the region\r\n" );
document.write( "outside of both circles:\r\n" );
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document.write( "The question is:\r\n" );
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\n" ); document.write( " What is the probability of randomly choosing a student who is not taking science?
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document.write( "These are the students in either a=28 or d=54.  That's 28+54 or 82 students\r\n" );
document.write( "that are not in the blue circle S.\r\n" );
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document.write( "So the probability is 82 out of 160 or \"82%2F160\" which reduces to \"41%2F80\".\r\n" );
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document.write( "Edwin

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