document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158083>Question 1158083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Finite Mathematics:\r<BR>\n" );
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document.write( "A contestant draws a sequence of three cards, one question per card, and tries to answer the three questions. There are three cards with history questions, six cards with literature questions, and eight cards with science questions. Find the probability of each of the following. (Round your answers to four decimal places.)<BR>\n" );
document.write( "(a) the questions are history, literature, and science, in that order<BR>\n" );
document.write( "(b) all three are literature questions<BR>\n" );
document.write( "(c) the first is science, the second is history, and the third is science </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854571 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5377)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> At first, there is a total of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2B6%2B8=17 ALIGN=MIDDLE  ALT=\"3%2B6%2B8=17\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw from.<BR>\n" );
document.write( "After the first card is drawn, there will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17-1=16 ALIGN=MIDDLE  ALT=\"17-1=16\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw from.<BR>\n" );
document.write( "After the first card and second have been drawn, there will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17-2=15 ALIGN=MIDDLE  ALT=\"17-2=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw from.<BR>\n" );
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document.write( "(a) Probability that the questions are history, literature, and science, in that order:<BR>\n" );
document.write( " <BR>\n" );
document.write( "At first,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17 ALIGN=MIDDLE  ALT=\"17\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw from, including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > history cards.<BR>\n" );
document.write( "The probability that the first card drawn is a history card is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F17 ALIGN=MIDDLE  ALT=\"3%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After that,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw the second card from, including all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > literature cards.<BR>\n" );
document.write( "The probability to draw a literature card after having drawn a history card is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F16=3%2F8 ALIGN=MIDDLE  ALT=\"6%2F16=3%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After that,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw the third card from, including all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > science cards. <BR>\n" );
document.write( "The probability to draw a science car after having drawn a history card followed by a literature car is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F15%29 ALIGN=MIDDLE  ALT=\"%288%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The probability that the questions are history, literature, and science, in that order is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F17%29%283%2F8%29%288%2F15%29=3%2A3%2A8%2F%2817%2A8%2A15%29=3%2F%2817%2A5%29=3%2F85=highlight%280.0353%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to four decimal places).\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "(b) Probability that all three cards drawn are literature questions:<BR>\n" );
document.write( " <BR>\n" );
document.write( "At first,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17 ALIGN=MIDDLE  ALT=\"17\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw from, including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > literature cards.<BR>\n" );
document.write( "The probability that the first card drawn is a literature card is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F17 ALIGN=MIDDLE  ALT=\"6%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After that,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw the second card from, including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-1=5 ALIGN=MIDDLE  ALT=\"6-1=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > literature cards.<BR>\n" );
document.write( "The probability to draw a second literature card after having drawn a literature card is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F16 ALIGN=MIDDLE  ALT=\"5%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After that,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw the third card from, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-2=4 ALIGN=MIDDLE  ALT=\"6-2=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > literature cards. <BR>\n" );
document.write( "The probability to draw a third literature card after two literature cards is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F15%29 ALIGN=MIDDLE  ALT=\"%284%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The probability that all three questions drawn are literature questions is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F17%29%285%2F16%29%284%2F15%29=6%2A5%2A4%2F%2817%2A16%2A15%29=120%2F4080=highlight%280.0314%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to four decimal places).\r<BR>\n" );
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document.write( " <BR>\n" );
document.write( "(c) Probability that the first card drawn is science, the second is history, and the third is science<BR>\n" );
document.write( " <BR>\n" );
document.write( "At first,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17 ALIGN=MIDDLE  ALT=\"17\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw from, including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > science cards.<BR>\n" );
document.write( "The probability that the first card drawn is a science card is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F17 ALIGN=MIDDLE  ALT=\"8%2F17\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After that,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw the second card from, including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > history cards and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-1=7 ALIGN=MIDDLE  ALT=\"8-1=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > science cards.<BR>\n" );
document.write( "The probability to draw a history card after having drawn a science card is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F16 ALIGN=MIDDLE  ALT=\"3%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "After that,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" > cards to draw the third card from, including <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8-1=7 ALIGN=MIDDLE  ALT=\"8-1=7\"   DISABLED_style= \"max-width:90%; height:auto;\" > science cards. <BR>\n" );
document.write( "The probability to draw a science card after having drawn a science card and a history card is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F15%29 ALIGN=MIDDLE  ALT=\"%287%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The probability that the first card drawn is science, the second is history, and the third is science is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288%2F17%29%283%2F16%29%287%2F15%29=8%2A3%2A7%2F%2817%2A16%2A15%29=168%2F4080=highlight%280.0412%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to four decimal places).<BR>\n" );
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