document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=663913>Question 663913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You pick 5 apples from a grocery store owned by the professor. The probability of a randomly chosen apple being rotten is 0.518. Let X represent the number of apples that are NOT rotten. Find the probability of X=k in the table below.\r<BR>\n" );
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document.write( "k 	P(X = k)<BR>\n" );
document.write( "0 	<BR>\n" );
document.write( "1 	<BR>\n" );
document.write( "2 	<BR>\n" );
document.write( "3 	<BR>\n" );
document.write( "4 	<BR>\n" );
document.write( "5 \r<BR>\n" );
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document.write( "I tried multiplying .482*0 then .482*1 all the way down the table.	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #413038 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=413038\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\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)\ =\ {{n}\choose{k}}\left(p\right)^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 {{n}\choose{k}}\"> 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)!}\">.  Hint: <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE {{n}\choose{0}}\ =\ {{n}\choose{n}}\ =\ 1\">.  Also <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE a^0\ =\ 1\">\r<BR>\n" );
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document.write( "You want:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_5(0,0.518)\ =\ {{5}\choose{0}}\left(0.518\right)^0\left(1\,-\,0.518\right)^{5\,-\,0}\">\r<BR>\n" );
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document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P_5(1,0.518)\ =\ {{5}\choose{1}}\left(0.518\right)^1\left(1\,-\,0.518\right)^{5\,-\,1}\">\r<BR>\n" );
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document.write( "and so on.\r<BR>\n" );
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document.write( "Happy calculator button punching.  If you have Excel on the PC or Numbers on the Mac, then enter =BINOMDIST(k, n, p, FALSE) replacing k, n, and p with the appropriate values.  The false means \"not cumulative\" and causes the function to return the probability of exactly k successes.  If you use TRUE, you get the probability of k or less.  =1 - BINOMDIST(k - 1, n, p, TRUE) gives you the probability of at least k successes.\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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