document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=393208>Question 393208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (1 pt) A card is drawn randomly from a standard 52-card deck. Find the probability of the given event. \r<BR>\n" );
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document.write( "(a) The card drawn is 9. <BR>\n" );
document.write( "The probability is:  \r<BR>\n" );
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document.write( "(b) The card drawn is a face card. <BR>\n" );
document.write( "The probability is:  \r<BR>\n" );
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document.write( "(c) The card drawn is not a face card. <BR>\n" );
document.write( "The probability is: \r<BR>\n" );
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document.write( "(1 pt) 4 cards are drawn at random from a standard deck. <BR>\n" );
document.write( "Find the probability that all the cards are hearts.   \r<BR>\n" );
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document.write( "Find the probability that all the cards are face cards.   <BR>\n" );
document.write( "Note: Face cards are kings, queens, and jacks. \r<BR>\n" );
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document.write( "Find the probability that all the cards are even.   <BR>\n" );
document.write( "(Consider aces to be 1, jacks to be 11, queens to be 12, and kings to be 13) <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 #279104 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=279104\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "The probability of anything is the number of ways that it can happen that you would consider a success divided by the number of ways it can happen total -- successes and failures.\r<BR>\n" );
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document.write( "There are 52 cards in the deck.  4 of them are 9s.\r<BR>\n" );
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document.write( "12 of them are face cards.\r<BR>\n" );
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document.write( "40 of them are not face cards.  (or just subtract the answer to the previous question from 1)\r<BR>\n" );
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document.write( "The probability of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> successes in <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> trials where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\"> is the probability of success on any given trial is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_n(k,p)\ =\ \left(n\cr k\right\)p^k\left(1\,-\,p\right)^{n\,-\,k}\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(n\cr k\right\)\"> is the number of combinations of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> things taken <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> at a time and is calculated by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{n!}{k!(n\,-\,k)!}\">\r<BR>\n" );
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document.write( "So for 4 hearts out of 4 cards dealt:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ =\ 4\ \ \">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\ =\ 4\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\ =\ \frac{1}{4}\">\r<BR>\n" );
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document.write( "So for 4 face cards out of 4 cards dealt:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ =\ 4\ \ \">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\ =\ 4\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\ =\ \frac{3}{13}\">\r<BR>\n" );
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document.write( "And for 4 even numbered cards out of 4 cards dealt:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ =\ 4\ \ \">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\ =\ 4\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large p\ =\ \frac{6}{13}\">\r<BR>\n" );
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document.write( "You get to do your own arithmetic.  Hint: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(n\cr n\right\)\ =\ 1\ \forall\ n\ >\ 0\ \in\ \mathbb{Z}\ \"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x^0\ =\ 1\ \forall\ x\ \in\ \mathbb{R}\"> \r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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