document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1043583>Question 1043583</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 14	The probability of winning a prize in game of chance is 0.2. The least number of games that must be played to ensure that the probability of winning at least one prize is more than 0.90 is closest to: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659045 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=659045\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The act of playing the game multiple times is a binomial experiment with p = 0.20.  <BR>\n" );
document.write( "The probability of winning at least one prize is given by the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28matrix%282%2C1%2Cn%2Ck%29%29%2A0.8%5E%28n-k%29%2A0.2%5Ek%2C+k+=+1%2Cn%29 ALIGN=MIDDLE  ALT=\"sum%28%28matrix%282%2C1%2Cn%2Ck%29%29%2A0.8%5E%28n-k%29%2A0.2%5Ek%2C+k+=+1%2Cn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Hence we want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+0.8%5En+=+sum%28%28matrix%282%2C1%2Cn%2Ck%29%29%2A0.8%5E%28n-k%29%2A0.2%5Ek%2C+k+=+1%2Cn%29+%3E+0.9 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > or \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-+0.8%5En+%3E+0.9 ALIGN=MIDDLE  ALT=\"1+-+0.8%5En+%3E+0.9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.10+%3E+0.8%5En ALIGN=MIDDLE  ALT=\"0.10+%3E+0.8%5En\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.10%29+%3E+ln+%280.8%5En%29+=+n%2Aln%280.80%29 ALIGN=MIDDLE  ALT=\"ln%280.10%29+%3E+ln+%280.8%5En%29+=+n%2Aln%280.80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since ln is an increasing function.\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%280.10%29%2Fln%280.80%29+=+10.31885116+%3C+n ALIGN=MIDDLE  ALT=\"ln%280.10%29%2Fln%280.80%29+=+10.31885116+%3C+n\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since ln(0.80) < 0.\r<BR>\n" );
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document.write( "===> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+%3C=+n ALIGN=MIDDLE  ALT=\"11+%3C=+n\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Therefore least number of games that must be played to ensure that the probability of winning at least one prize is more than 0.90 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2811%29 ALIGN=MIDDLE  ALT=\"highlight%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </SPAN>\n" );
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