document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=847473>Question 847473</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the probability of any one outcome\r<BR>\n" );
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document.write( "n = 5, x = 2, p = 0.646\r<BR>\n" );
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document.write( "n = 11, x = 9, p = 0.42\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #510468 by </B><A HREF=/tutors/aboutme.mpl?userid=swincher4391><B>swincher4391(1107)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=swincher4391><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=swincher4391><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=510468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is the binomial distribution and basically all that is happening is that you are choosing x successes out of n total trials. Since all are independent, we can just multiply the resulting probabilities. The other trials [n-x trials] that are failures are counted as 1-p.  So, to summarize, out of x chosen successes out of n, we multiply the probability of success x times, and the probability of failure the other n-x times.\r<BR>\n" );
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document.write( "So in general we have the formula (n choose x) * (p)^x * (q)^(n-x) where q = 1-p\r<BR>\n" );
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document.write( "1.\r<BR>\n" );
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document.write( "(5 choose 2) * (.646)^2 * (1-.646)^3  = .1851\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "(11 choose 9) * (.42)^9 * (1-.42)^2 = .0075 </SPAN>\n" );
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