document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1028530>Question 1028530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 20 people in a room, and each of the 20 writes down an integer at random from 1-100 inclusive. Find the probability that at least two people wrote down the same number. Express your answer as a decimal rounded to four significant digits.\r<BR>\n" );
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document.write( "This is not so complicated; however, how do I \"determine the probability of AT LEAST TWO PEOPLE\" drawing the same number?\r<BR>\n" );
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document.write( "Thank you in advance!!\r<BR>\n" );
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document.write( "By the way, the answer is 0.8696 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #643615 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=643615\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 100 P 20 = 1.303995*10^39 different ways to have 20 people pick different numbers (from a pool of 100). No repeated numbers allowed.\r<BR>\n" );
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document.write( "Note: 100 P 20 is referring to a <a  rel=nofollow HREF=\"http://www.regentsprep.org/regents/math/algebra/apr2/lperm.htm\">permutation</a> \r<BR>\n" );
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document.write( "There are 100^20 = 1*10^40 different ways for 20 people to pick any number they want (repeats are now allowed) \r<BR>\n" );
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document.write( "The probability of 20 people picking different numbers (no repeats) is<BR>\n" );
document.write( "(1.303995*10^39)/(1*10^40) = 0.1303995\r<BR>\n" );
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document.write( "Subtract this from 100%, which is equivalent to the decimal form 1.00, so\r<BR>\n" );
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document.write( "1.00 - 0.1303995 = 0.8696005 which rounds to 0.8696\r<BR>\n" );
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document.write( "I'm subtracting from 100% because there are 2 choices<BR>\n" );
document.write( "either you have a case where everyone picks different numbers (no repeats)<BR>\n" );
document.write( "OR<BR>\n" );
document.write( "there is a case where some people pick the same number(s) (repeats allowed). Whether who or how many, it doesn't matter. <BR>\n" );
document.write( "There are no other possible cases. These two probabilities add to 100%\r<BR>\n" );
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document.write( "Therefore, the final answer is approximately 0.8696 which is approximately 86.96% </SPAN>\n" );
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