document.write( "Question 1162354: Among the class of 100 students, 75 studied Botany, 55 studied Biology and 40 students
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Algebra.Com's Answer #786139 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Among the class of 100 students,
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document.write( "So a+b+c+d = 100\r\n" );
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75 studied Botany,
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document.write( "So a+b = 75\r\n" );
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55 studied Biology
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document.write( "So b+c = 55\r\n" );
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and 40 students studied both of the subjects.
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document.write( "So b=40\r\n" );
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document.write( "Substituting 40 for b in b+c = 55\r\n" );
document.write( "                        40+c = 55\r\n" );
document.write( "                           c = 15\r\n" );
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document.write( "Substituting 40 for b in a+b = 75\r\n" );
document.write( "                        a+40 = 75\r\n" );
document.write( "                           a = 35\r\n" );
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document.write( "Substituting a=35, b=40, and c=15 in\r\n" );
document.write( "                     a+b+c+d = 100\r\n" );
document.write( "                  35+40+15+d = 100\r\n" );
document.write( "                        90+d = 100\r\n" );
document.write( "                           d = 10\r\n" );
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A student is selected at random from this class what is the
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document.write( "All but the 10.  So that's 100-10 = 90 out of 100, so the probability\r\n" );
document.write( "is 90/100 which reduces to 9/10\r\n" );
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ii) student studied Botany but not Biology
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document.write( "That's the 35.  So that's 35 out of 100, so the probability\r\n" );
document.write( "is 35/100 which reduces to 7/20\r\n" );
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iii) student studied Biology but not Botany.
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document.write( "That's the 15.  So that's 15 out of 100, so the probability\r\n" );
document.write( "is 15/100 which reduces to 3/20\r\n" );
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iv) student studied none of the subjects
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document.write( "That's the 10 that aren't in either circle.  So that's 10 out of 100, \r\n" );
document.write( "so the probability is 10/100 which reduces to 1/10.\r\n" );
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document.write( "Edwin
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