document.write( "Question 1138803: A survey of 448 students at a small college showed that 234 students responded
\n" ); document.write( "that they did not like to ski, 100 students responded that they played hockey,
\n" ); document.write( "and that there were 189 students the neither skied nor played hockey. Without
\n" ); document.write( "the use of a Venn Diagram, determine the probability that a randomly selected
\n" ); document.write( "student both skied and played hockey. Make sure that you define all the
\n" ); document.write( "appropriate sets needed to solve the problem, convert the phrases in the above
\n" ); document.write( "sentences to set theoretic notation, and show the steps. \n" ); document.write( "

Algebra.Com's Answer #756702 by Edwin McCravy(20077) $\"\"$ $\"About$

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A survey of 448 students at a small college showed that 234 students responded
\n" ); document.write( "that they did not like to ski, 100 students responded that they played hockey,
\n" ); document.write( "and that there were 189 students the neither skied nor played hockey. Without
\n" ); document.write( "the use of a Venn Diagram, determine the probability that a randomly selected
\n" ); document.write( "student both skied and played hockey. Make sure that you define all the
\n" ); document.write( "appropriate sets needed to solve the problem, convert the phrases in the above
\n" ); document.write( "sentences to set theoretic notation, and show the steps.
\n" ); document.write( "

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document.write( "Even though you are not to use a Venn diagram, use one privately anyway to get\r\n" );
document.write( "the idea right and then set up the equations. Don't turn in the Venn diagram.\r\n" );
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document.write( "Let a = n(SᑎH')\r\n" );
document.write( "Let b = n(SᑎH)\r\n" );
document.write( "Let c = n(S'ᑎH)\r\n" );
document.write( "Let d = n(S'ᑎH')\r\n" );
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document.write( ">>A survey of 448 students at a small college...<<\r\n" );
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document.write( "a+b+c+d = 448 = n(U) = n(SᑎH') + n(SᑎH) + n(S'ᑎH) + n(S'ᑎH')\r\n" );
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document.write( ">>...showed that 234 students responded that they did not like to ski,...<<\r\n" );
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document.write( "c+d = 234 = n(S'ᑎH) + n(S'ᑎH')\r\n" );
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document.write( ">>100 students responded that they played hockey,<< \r\n" );
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document.write( "b+c = 100 =n(SᑎH) + n(S'ᑎH) \r\n" );
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document.write( ">>and that there were 189 students the neither skied nor played hockey.<< \r\n" );
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document.write( "d = 189 = n(S'ᑎH')\r\n" );
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document.write( "So we have the system of equations:\r\n" );
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document.write( "Solve that system by substitution (that's easy), getting \r\n" );
document.write( "a=159, b=55, c=45, d=189\r\n" );
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document.write( "Then the desired probability is \r\n" );
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document.write( "b/(a+b+c+d) = n(SᑎH)/n(U) = 55/448\r\n" );
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document.write( "Edwin

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