document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=343367>Question 343367</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If three people are randomly sampled, what is the probability that one is born on your birthday? (assume 365 days in a year).\r<BR>\n" );
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document.write( "I got:   3/365 = .82% ...... This doesn't even look right to me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #245690 by </B><A HREF=/tutors/aboutme.mpl?userid=nyc_function><B>nyc_function(2741)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nyc_function><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=nyc_function><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=245690\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The answer is 398,581/48,627,125 or approximately 0.0082.\r<BR>\n" );
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document.write( "Call the people Al, Betty, and Chuck.\r<BR>\n" );
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document.write( "The probability that Al isn't born on your birthday is 364/365. Likewise for Betty and Chuck.\r<BR>\n" );
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document.write( "These three probabilities are independent (knowing Al's birthday doesn't influence your probability for Betty), so we can find the probability that *none* of these people share your birthday by multiplying:<BR>\n" );
document.write( "364/365 * 364/365 * 364/365 = 48,228,544/48,627,125.\r<BR>\n" );
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document.write( "But we want the probability that one of these people *does* share your birthday. This is exactly the negation of the event that none of them share your birthday, so the probability is one minus that;<BR>\n" );
document.write( "1 - 48,228,544/48,627,125 = 398,581/48,627,125.\r<BR>\n" );
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document.write( "Another approach to this problem: there are 48,627,125 possible arrangements of these people's birthdays (365*365*365). Of these, there are (1*365*365 + 364*1*365 + 364*364*1), or 398,581, arrangements in which at least one person shares your birthday. So, the probability of that event is 398,581/48,627,125.<BR>\n" );
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