document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044884>Question 1044884</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A homeowner's association meeting, a board member can vote yes vote no or abstain from a motion. There are three motions on which dashboard member must vote. Determine the number of points in a sample space. Determine the probability that a board member votes yes on all of the motions. Determine the probability that a board member votes yes on at least one. (Simplify fractions) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660304 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=660304\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Y = member votes yes<BR>\n" );
document.write( "N = member votes no<BR>\n" );
document.write( "A = member abstains\r<BR>\n" );
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document.write( "Sample Space<BR>\n" );
document.write( "YYY<BR>\n" );
document.write( "YYN<BR>\n" );
document.write( "YYA<BR>\n" );
document.write( "YNY<BR>\n" );
document.write( "YNN<BR>\n" );
document.write( "YNA<BR>\n" );
document.write( "YAY<BR>\n" );
document.write( "YAN<BR>\n" );
document.write( "YAA\r<BR>\n" );
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document.write( "NYY<BR>\n" );
document.write( "NYN<BR>\n" );
document.write( "NYA<BR>\n" );
document.write( "NNY<BR>\n" );
document.write( "NNN<BR>\n" );
document.write( "NNA<BR>\n" );
document.write( "NAY<BR>\n" );
document.write( "NAN<BR>\n" );
document.write( "NAA\r<BR>\n" );
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document.write( "AYY<BR>\n" );
document.write( "AYN<BR>\n" );
document.write( "AYA<BR>\n" );
document.write( "ANY<BR>\n" );
document.write( "ANN<BR>\n" );
document.write( "ANA<BR>\n" );
document.write( "AAY<BR>\n" );
document.write( "AAN<BR>\n" );
document.write( "AAA\r<BR>\n" );
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document.write( "Those are all the possible outcomes. There are 27 items in the sample space above. There's only one case of YYY out of the 27 cases total. So the probability of voting all yes is 1/27.\r<BR>\n" );
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document.write( "There are 8 cases where Y doesn't show up at all. Those cases are\r<BR>\n" );
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document.write( "NNN<BR>\n" );
document.write( "NNA<BR>\n" );
document.write( "NAN<BR>\n" );
document.write( "NAA\r<BR>\n" );
document.write( "\n" );
document.write( "ANN<BR>\n" );
document.write( "ANA<BR>\n" );
document.write( "AAN<BR>\n" );
document.write( "AAA\r<BR>\n" );
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document.write( "This means there are 27-8 = 19 cases where Y shows up at least once. \r<BR>\n" );
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document.write( "So the probability of voting at least one yes (Y) is 19/27\r<BR>\n" );
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document.write( "-------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Summary:\r<BR>\n" );
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document.write( "The answer to the problem <font color=blue>\"Determine the number of points in a sample space.\"</font> is <font color=red>27</font> \r<BR>\n" );
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document.write( "The answer to the problem <font color=blue>\"Determine the probability that a board member votes yes on all of the motions.\"</font> is the fraction <font color=red>1/27</font> \r<BR>\n" );
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document.write( "The answer to the problem <font color=blue>\"Determine the probability that a board member votes yes on at least one.\"</font> is the fraction <font color=red>19/27</font> \r<BR>\n" );
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document.write( "</font> </SPAN>\n" );
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