document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394013>Question 394013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> n coins are simultaneously flipped. The probability that at most one of them shows tails is 3/16. Find n. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279561 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=279561\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The probability that at most one of n coins show tails is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=nC0%2A%281%2F2%29%5En%2A%281%2F2%29%5E0+%2B+nC1%2A%281%2F2%29%5E%28n-1%29%2A%281%2F2%29%5E1 ALIGN=MIDDLE  ALT=\"nC0%2A%281%2F2%29%5En%2A%281%2F2%29%5E0+%2B+nC1%2A%281%2F2%29%5E%28n-1%29%2A%281%2F2%29%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5En+%2B+n%281%2F2%29%5En ALIGN=MIDDLE  ALT=\"%281%2F2%29%5En+%2B+n%281%2F2%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%281%2F2%29%5En ALIGN=MIDDLE  ALT=\"%28n%2B1%29%281%2F2%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now the above sequence STRICTLY DECREASES as n INCREASES, because\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%2F2%5En+%3C+n%2F2%5E%28n-1%29+ ALIGN=MIDDLE  ALT=\"%28n%2B1%29%2F2%5En+%3C+n%2F2%5E%28n-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n+%3E+1 ALIGN=MIDDLE  ALT=\"n+%3E+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Values for n =1,2,3,4,5 will not satisfy  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%281%2F2%29%5En+=+3%2F16 ALIGN=MIDDLE  ALT=\"%28n%2B1%29%281%2F2%29%5En+=+3%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but n = 6 will.  Since the sequence <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2B1%29%281%2F2%29%5En ALIGN=MIDDLE  ALT=\"%28n%2B1%29%281%2F2%29%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" > is strictly decreasing, 6 is the only value of n that will satisfy the problem.\r<BR>\n" );
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document.write( "Therefore there were 6 coins. </SPAN>\n" );
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