document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=326869>Question 326869</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the probability of drawing one 5 from a pack of cards if you are dealt 4 cards?        And\r<BR>\n" );
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document.write( "If 3 dice are rolled what is the probability of throwing one 6.<BR>\n" );
document.write( "And what is the probability of throwing two 6's.\r<BR>\n" );
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document.write( "I would be very very grateful to see your working out for these questions </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #234090 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=234090\">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( "Since there are four 5s in the deck of 52 the probability of getting a 5 dealt to you on one draw is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{4}{52}\ =\ \frac{1}{13}\">.\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( "You want exactly 1 success out of 4 trials where the probability of success on one trial is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{13}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_4\left(1,\frac{1}{13}\right)\ =\ \left(4\cr 1\right\)\left(\frac{1}{13}\right)^1\left(\frac{12}{13}\right)^{3}\">\r<BR>\n" );
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document.write( "You can do your own arithmetic.  Hint <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(n\cr 1\right\)\ =\ n\">.\r<BR>\n" );
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document.write( "By the way, note that this is the probability of getting exactly one 5, no more, no less.  If you want to know the probability of <i><b>at least</b></i> one 5, that is another thing altogether.  In that case you could calculate the cumulative probability, that is the probability of one 5 plus the probability of two 5s, and so on:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_4\left(\geq 1,\frac{1}{13}\right)\ =\ \sum_{i\,=\,1}^4\ \left(4\cr i\right\)\left(\frac{1}{13}\right)^i\left(\frac{12}{13}\right)^{4-i}\">\r<BR>\n" );
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document.write( "Or you could realize that \"at least 1\" means \"any outcome except 0\" and then calculate the probability of getting no 5s at all and then subtracting that number from 1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ P_4\left(0,\frac{1}{13}\right)\ =\ \left(4\cr 0\right\)\left(\frac{1}{13}\right)^0\left(\frac{12}{13}\right)^{4}\">\r<BR>\n" );
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document.write( "Hint:  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(n\cr 0\right\)\ =\ 1\"> and anything raised to the zero power is 1.\r<BR>\n" );
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document.write( "Your other problem is done the same way.  You just need to calculate <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P_3\left(1,\frac{1}{6}\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE P_3\left(2,\frac{1}{6}\right)\">\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" );
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