document.write( "Question 1143803: 32 of the 80 members of a club are married and of these, 8 are managers. There are 20 managers in total in the club.
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Algebra.Com's Answer #764712 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let M be the subset of members of a club that are married.  \r\n" );
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document.write( "    The number of members in this subset is n(M) = 32.\r\n" );
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document.write( "Let G be the subset of members of a club that are managers.\r\n" );
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document.write( "    The number of members in this subset is n(G) = 20.\r\n" );
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document.write( "The intersection  MG = (M & G)  are those members that are married and are managers.\r\n" );
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document.write( "    This subset has 8 persons : n(M & G) = 8.\r\n" );
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document.write( "(i)   Find the probability that a person chosen at random is a married manager equals  P =  =  = 0.1 = 10%.    ANSWER\r\n" );
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document.write( "(ii) The set of those who is EITHER married OR manager is the UNION of the sets M and G, i.e. (M U G).\r\n" );
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document.write( "     It has  n(M U G) elements,  n(M U G) = n(M) + n(G) - n(M & G) = 32 + 20 - 8 = 44.   (1)\r\n" );
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document.write( "    The rest of the members in the club are NEITHER married NOR managers,\r\n" );
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document.write( "    and their number is  80 - 44 = 36.    \r\n" );
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document.write( "    Therefore, the answer to ii) is  P =  =  = 0.45 = 45%.   ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "The proof of the formula (1) is easy: the number of elements of the union of any two finite subsets of a universal set \r
\n" ); document.write( "\n" ); document.write( "is always equal to the sum of elements of the subsets minus number of elements in their intersection.\r
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\n" ); document.write( "\n" ); document.write( "On this subject, see the lesson\r
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