document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189397>Question 1189397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Anna flips 8 coins, what is the probability that she gets more heads than tails?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #820748 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=820748\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Technically, the problem needs to state that the coins are fair coins.  Assuming that is the case....<br><BR>\n" );
document.write( "The probability of equal numbers of heads and tails (4 each) is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%288%2C4%29%2F2%5E8=70%2F256 ALIGN=MIDDLE  ALT=\"C%288%2C4%29%2F2%5E8=70%2F256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the probability of NOT getting 4 of each is 186/256.<br><BR>\n" );
document.write( "Then, since the probability of getting more heads than tails is the same as the probability of getting more tails than heads, the probability of getting more heads than tails is 93/256.<br><BR>\n" );
document.write( "ANSWER: 93/256<br><BR>\n" );
document.write( "Of course, you can also answer the problem by finding the probabilities of getting 5, or 6, or 7, or 8 heads:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28C%288%2C5%29%2BC%288%2C6%29%2BC%288%2C7%29%2BC%288%2C8%29%29%2F2%5E8=%2856%2B28%2B8%2B1%29%2F256=93%2F256 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Finally, you can answer a problem like this quickly if you know how to write out the 8th row of Pascal's Triangle:<br><BR>\n" );
document.write( "1 8 28 56 70 56 28 8 1<br><BR>\n" );
document.write( "Those numbers are C(8,8), C(8,7), ..., C(8,1), and C(8,0).  The sum of all those numbers is 2^8=256.  So the number of ways of getting more heads than tails is 1+8+28+56=93; and the probability of getting more heads than tails is 93/256.<br><BR>\n" );
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