document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257819>Question 257819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A balanced coin is tossed 8 times.  What is the probability of getting exactly 2 heads given that there were at least 2 heads in the 8 tosses? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189725 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189725\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let h=.5 and t=.5, probability of heads or tails.<BR>\n" );
document.write( "We need to find a number in the expansion of the binomial (h+t)^8<BR>\n" );
document.write( "We are looking for h^2t^6<BR>\n" );
document.write( "The coefficient is nCr=8C2=28 Combination<BR>\n" );
document.write( "28h^2t^6=28*.25*.0156=.1094 prob of exactly 2 heads.<BR>\n" );
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document.write( "1-t^8-8t^7h=1-.0039-(8*.0078*.5)<BR>\n" );
document.write( "=1-.0039-.03125<BR>\n" );
document.write( "=.9649 prob of at least 2 heads.<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".1094/.9649=.1134 probability of getting exactly 2 heads given that there were at least 2 heads in the 8 tosses.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Ed </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );