document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1092525>Question 1092525</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the probability that in tossing a fair coin 9 times, there will appear:<BR>\n" );
document.write( "1. 6 tails<BR>\n" );
document.write( "2. 5 heads<BR>\n" );
document.write( "3. at least 2 tails<BR>\n" );
document.write( "4. not more than 3 heads </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #707148 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=707148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The general form of this kind of problem is nCr*p^r*(1-p)^(n-r). Here, p and 1-p are both a half, so the terms p^r*(1-p)^(n-r) are really (1/2)^9 or 1/518.  <BR>\n" );
document.write( "For 9C0, the probability of 0 heads (or 0 tails, if one wishes), it is 1<BR>\n" );
document.write( "for 9C1, the probability of 1, it is 9!/1!*8!=9<BR>\n" );
document.write( "and so forth.\r<BR>\n" );
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document.write( "6 tails is 9C6(1/2)^6((1/2)^3<BR>\n" );
document.write( "84/512=0.1641<BR>\n" );
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document.write( "5 heads is 9C5(1/2)^5(1/2)^4=126/512=0.2461<BR>\n" );
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document.write( "at least 2 tails is 1- p(1 tail)-p(0) tails)<BR>\n" );
document.write( "p(1) is 9/512 and p(0) is 1/512<BR>\n" );
document.write( "it is 502/512 or 0.9805<BR>\n" );
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document.write( "not more than 3 heads is p(0)+p(1)+p(2)+p(3)<BR>\n" );
document.write( "this is over a denominator of 512 (the 1/2^x*(1/2)^9-x<BR>\n" );
document.write( "p(0) has a numerator of 1, p(1) has 9 p(2) has 9C2=36, and p(3) has 9C3 as a numerator, or 84<BR>\n" );
document.write( "the probability is 130/512 or 0.2539 </SPAN>\n" );
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