document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170141>Question 1170141</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The black face cards and the red cards numbered 3-7 are put into a bag.  4 cards are drawn at random without replacement.  Find the probability that…\r<BR>\n" );
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document.write( "2 cards are black and 2 cards are red.\r<BR>\n" );
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document.write( "All cards are red.\r<BR>\n" );
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document.write( "At least 1 of the cards is black.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794999 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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/cgi-bin/show-face.mpl?user=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=794999\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> An easier way to say this is that there are 6 black cards and 10 red cards.<BR>\n" );
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document.write( "<i>a) Probability that 2 cards are black and 2 cards are red</i><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286C2+%2A+10C2%29%2F%2816C4%29 ALIGN=MIDDLE  ALT=\"%286C2+%2A+10C2%29%2F%2816C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%21%2F%282%21%2A4%21%29%29%2A%2810%21%2F%282%21%2A8%21%29%29%2F%2816%21%2F%284%21%2A12%21%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815+%2A+45%29%2F1820 ALIGN=MIDDLE  ALT=\"%2815+%2A+45%29%2F1820\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=675%2F1820 ALIGN=MIDDLE  ALT=\"675%2F1820\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=135%2F364 ALIGN=MIDDLE  ALT=\"135%2F364\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.3709<BR>\n" );
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document.write( "<i>b) Probability that all the cards are red</i><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810C4%29%2F%2816C4%29 ALIGN=MIDDLE  ALT=\"%2810C4%29%2F%2816C4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%21%2F%284%21%2A6%21%29%29%2F%2816%21%2F%284%21%2A12%21%29%29 ALIGN=MIDDLE  ALT=\"%2810%21%2F%284%21%2A6%21%29%29%2F%2816%21%2F%284%21%2A12%21%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2F1820 ALIGN=MIDDLE  ALT=\"210%2F1820\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F26 ALIGN=MIDDLE  ALT=\"3%2F26\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.1154<BR>\n" );
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document.write( "<i>c) Probability that at least 1 of the cards is black<BR>\n" );
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document.write( "For this problem, you want to calculate the odds that NONE of the cards are  black, then subtract this result from 1.<BR>\n" );
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document.write( "\"None of the cards are black\" is exactly the same thing as \"all of the cards are red\".  In question 'b' above, we've already calculated the probability that all of the cards are red.  So, we simply subtract this result from 1 to find out the probability that \"at least 1 of the cards is black\".<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+0.1154 ALIGN=MIDDLE  ALT=\"1+-+0.1154\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.8846 </SPAN>\n" );
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