document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=510573>Question 510573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the probability that in a class of 8 students, at least two students have the same birthday. Assume that there are always 365 days in a year and that birth rates are constant throughout the year. (Hint: First determine the probability that no two students have the same birthday and then apply the complementation rule.)\r<BR>\n" );
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document.write( "Please help! Thanks, Sue </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341840 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=341840\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Determine the probability that in a class of 8 students, at least two students have the same birthday. Assume that there are always 365 days in a year and that birth rates are constant throughout the year. (Hint: First determine the probability that no two students have the same birthday and then apply the complementation rule.) \r<BR>\n" );
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document.write( "1st: 1<BR>\n" );
document.write( "2nd: (1-(1/365)) = (364/365<BR>\n" );
document.write( "3rd: (1-(2/365)) = (363/365<BR>\n" );
document.write( "4th: (1-(3/365)) = (362/365<BR>\n" );
document.write( "...<BR>\n" );
document.write( "8th: (1-(7/365)) = (358/365)<BR>\n" );
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document.write( "P(no 2 of 8 have the same birthday) = [1(364)(363)(362)...(358)]/365^7<BR>\n" );
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document.write( "= 0.9257<BR>\n" );
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document.write( "P(2 have the same birthday) = 1 - 0.9257 = 0.0743<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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