document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108079>Question 1108079</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A coin is flipped four times. Find the probability of getting two heads and two tails. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #723091 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=723091\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Intuition says it should be  0.50, and that is unfortunately incorrect in this case.\r<BR>\n" );
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document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%5E4+=+16+ ALIGN=MIDDLE  ALT=\"+2%5E4+=+16+\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible outcomes.\r<BR>\n" );
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document.write( "Breaking it down into groups of two:\r<BR>\n" );
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document.write( "HH  —> Only TT can follow this<BR>\n" );
document.write( "HT  —>  Only HT or TH can follow this<BR>\n" );
document.write( "TH   —>  Only HT or TH can follow this <BR>\n" );
document.write( "TT  —>  Only HH can follow this\r<BR>\n" );
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document.write( "So out of 16 possible outcomes, only 6 have exactly two heads and two tails.  \r<BR>\n" );
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document.write( "The probability of getting two heads and two tails is then  6/16 = <b>3/8</b>\r<BR>\n" );
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document.write( "—<BR>\n" );
document.write( "An alternative way to look at this: there are 4 slots for each of the 4 flips, and we want heads to occupy exactly 2 of them:  C(4,2) = 4!/(2!*2!) = 24/4 = 6,  and dividing by the 16 possible outcomes, that computes to a probability of 6/16 = 3/8.\r<BR>\n" );
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