document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=926433>Question 926433</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In an experiment, a fair coin is tossed 13 times and the face that appears (H for head or T for tail) for each toss is recorded.<BR>\n" );
document.write( "1.How many elements of the sample space will start with a pair (TT or HH ) or end with a pair (but not both) and have a total of exactly two heads?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #562939 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=562939\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the 13-tuple starts or ends with HH, then the remaining 11 flips must be T, but this violates the constraint that it cannot both start and end with a pair, so zero tuples. Therefore it must start with TT and end with TH or HT, or start with TH or HT and end TT.\r<BR>\n" );
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document.write( "If we start with TT and end with TH or HT, there are 2 ways to pick TH or HT, and then out of 9 remaining slots, one of them will be H. So 2*9 = 18 ways. Same with ending with TT/starting with TH or HT. Overall there are 36 ways. </SPAN>\n" );
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