document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124876>Question 1124876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A fair coin is tossed nine times, with the result (H or T) of each flip noted. \r<BR>\n" );
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document.write( "How many outcomes does the experiment have?  \r<BR>\n" );
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document.write( "How many outcomes are there where heads comes up three times?  \r<BR>\n" );
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document.write( "What is the probability of the outcome HHHTTTTTT?  <BR>\n" );
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document.write( "What is the probability that heads comes up three times?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #741166 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=741166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2^9 = 512 outcomes<BR>\n" );
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document.write( "the binomial probability formula is<BR>\n" );
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document.write( "Probability (P) ( k successes in n trials ) = nCk * p^k * (1-p)^(n-k), where nCk =  n!/k!(n-k)!, p is probability of success<BR>\n" );
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document.write( "if k = 3, then<BR>\n" );
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document.write( "P (3 heads in 9 trials) = 9C3 * (1/2)^3 * (1-(1/2))^(9-3) =<BR>\n" );
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document.write( "9!/3!(9-3)! * (1/8) * (1/64) =<BR>\n" );
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document.write( "(9*8*7/(3*2)) * (1/512) =<BR>\n" );
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document.write( "84/512<BR>\n" );
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document.write( "There are 84 outcomes where heads comes up three times<BR>\n" );
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document.write( "P of HHHTTTTTT = (1/2)^3 * (1/2)^6 = (1/8) * (1/64) = 1/512<BR>\n" );
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document.write( "P heads comes up three times is 84/512 = 21/128<BR>\n" );
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