document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203189>Question 1203189</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A recent study of robberies for a certain geographic area showed an average of 1 robbery per 20,000 people. In a city of 80,000 people, find the probability of the following...\r<BR>\n" );
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document.write( "a) 0 robberies\r<BR>\n" );
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document.write( "b) 1 robbery	\r<BR>\n" );
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document.write( "c) 2 robberies \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838556 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838556\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assuming this is a binomial distribution, i get the following:\r<BR>\n" );
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document.write( "n = 80,000<BR>\n" );
document.write( "p = 1/20,000 = .00005<BR>\n" );
document.write( "q = (1 - 1/20,000) = .99995<BR>\n" );
document.write( "x = 0, 1, or 2\r<BR>\n" );
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document.write( "formula is p(x) = p^x * q^(n-x) * c(n,x)\r<BR>\n" );
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document.write( "we get:\r<BR>\n" );
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document.write( "p(0) = .00005^0 * .99995^(80,000 - 0) * c(80,000,0) = 0.018313807.\r<BR>\n" );
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document.write( "p(1) = .00005^1 * .99995^(80,000 - 1) * C(80,000,1) = 0.073258892.\r<BR>\n" );
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document.write( "P(2) = .00005^2 * .99995^(80,000 - 2) * C(80,000,2) = 0.146523279.\r<BR>\n" );
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document.write( "the combination formula is c(n,x) = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "for example, when n = 80,000 and x = 2, this formula becomes:<BR>\n" );
document.write( "c(80,000,2) = 80,000 / (2! * 79,998!) which becomes:<BR>\n" );
document.write( "c(80,000,2) = (80,000 * 79,999 * 79,998!) / (2! * 79,998!) which becomes:<BR>\n" );
document.write( "c(80,000,2) = (80,000 * 79,999) / 2 = 3,199,960,000.\r<BR>\n" );
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document.write( "P(2) = .00005^2 * .99995^(80,000 - 2) * C(80,000,2) = 0.146523279 becomes:<BR>\n" );
document.write( "P(2) = .00005^2 * .99995^(80,000 - 2) * 3,199,960,000 = 0.146523279.<BR>\n" );
document.write( "you can verify with your calculator that this is correct.\r<BR>\n" );
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