document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=918207>Question 918207</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The planet Kepler-166 has an orbital period of 229 days. Consider a group of 20<BR>\n" );
document.write( "inhabitants on this planet. What is the probability that at least 2 of them share a<BR>\n" );
document.write( "birthday? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557016 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=557016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large P(\phi)\"> be the probability that no two people share a birthday.\r<BR>\n" );
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document.write( "If you have 2 people, then the probability the second person has a different birthday than the first person, given 229 possible birthdays, is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{228}{229}\">.  For the third person, the probability that the third birthday differs from that of both the first and second is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{228}{229}\ \cdot\ \frac{227}{229}\">\r<BR>\n" );
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document.write( "Following the same line of reasoning, the probability that none of the first twenty people share a birthday is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ P(\phi)\ =\ \prod_{i=0}^{19}\,\frac{229\ -\ i}{229}\">\r<BR>\n" );
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document.write( "Since \"at least 2\" is the complement of \"none\", the probability you want is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ P(\phi)\">\r<BR>\n" );
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document.write( "You can do your own calculator work.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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