document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185196>Question 1185196</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey of club membership of students, it is found that: 50% belongs to Club A, 55%<BR>\n" );
document.write( "belong to Club B, 60% belong to Club C, 30% belong to Club A and B, 25% belong to Club<BR>\n" );
document.write( "B and C, 20% belong to Club A and C, and 5% belong to all three Clubs. A.) What per cent<BR>\n" );
document.write( "belong to exactly two clubs? B.) What per cent do not belong to any club? </SPAN>\n" );
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document.write( "A survey of club membership of students, it is found that: 50% belongs to Club A, 55%<BR>\n" );
document.write( "belong to Club B, 60% belong to Club C, 30% belong to Club A and B, 25% belong to Club<BR>\n" );
document.write( "B and C, 20% belong to Club A and C, and 5% belong to all three Clubs. <BR>\n" );
document.write( "A) What percent belong to exactly two clubs? <BR>\n" );
document.write( "B) What percent do not belong to any club?<BR>\n" );
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document.write( "<H3>Part A)</H3>\r<BR>\n" );
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document.write( "Belong to A &#8745; B, but not C:  P ((AB) \ ABC) = 30% - 5% = 25%.\r\n" );
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document.write( "Belong to A &#8745; C, but not B:  P ((AC) \ ABC) = 20% - 5% = 15%.\r\n" );
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document.write( "Belong to B &#8745; C, but not A:  P ((BC) \ ABC) = 25% - 5% = 20%.\r\n" );
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document.write( "Now  the answer to question A)  is the sum  25% + 15% + 20% = 60%.    <U>ANSWER</U>\r\n" );
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document.write( "Part A) is solved, answered and explained.\r<BR>\n" );
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document.write( "<H3>Part B)</H3>\r<BR>\n" );
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document.write( "Apply the inclusion-exclusion principle\r\n" );
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document.write( "    P(A U B U C) = P(A) + P(B) + P(C) - P(AB) - P(AC) - P(BC) + P(ABC) =\r\n" );
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document.write( "                 = 50%  + 55%  + 60%  - 30%   - 20%   - 25%   + 5% = 95%.\r\n" );
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document.write( "THEREFORE, the remaining 5% do not belong any club.     <U>ANSWER</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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